5

(a) Solve dy = xBy by dx separation of variables:...

Question

(a) Solve dy = xBy by dx separation of variables:

(a) Solve dy = xBy by dx separation of variables:



Answers

Solve the differential equation.
$ \frac {dy}{dx} = x \sqrt y $

This question asked us to solve the differential equation three. X squared y squared Not what we know is that if this is r d y o ver de axe than r D y over, why squared is three x squared DX. This allows us to get the X is on the same side and the wise on the same side. No, let's take the integral. The integral of this is negative one over. Why be integral off this increased exports by one divide by the new exponents is execute. Don't forget our constant of integration plus C now lastly to right this just in terms of why we get wise negative one divided by X cubed plus sissy

This probable were given any question. And whereas isn't transition time there itself? Why X So we're gonna take their took old terms with respect. Ex starting from likeness that you have each of the excellent boy. But by buying narrative Oh, he function Excell. Why now? They're right inside. So we have won by this by the ex. He have you i d x. Because why the bunch of next? All right, so for this term right here, we're going to use caution. But also, we have each of the ex awhile mudslide by, um, the 1st 1 chin looks like by fortune the denominator y minus first function both blocked by the function you nominator divided by function that is equal to or minus D by he X. So let's group old terms with divine e X on one side. Um, less bird strike this morning as each of the excellent Why multiply by one Weisberg minus X over. Wife spirit must buy. Buy each of that. So why he won? Yes, that is equal to one months. He Why the X? Okay, so now we are ready to group over time. Do you have any eggs on one side. So we had you mind? Yes. Oh, um X over wine sprayed each of the excellent. Why? Minus one. And that is equal to each of the excellent wine or water minus one. All right, we can then, right? Do you want guys to be equal to, um, e to the X over? Why, minus one? There's something you wanted by. Why divide this by X times Each of the excellent wine minus voice. Greg, you like? Why spread? This was just, like ever went up for so that we will find the answer to be you want. The X is equal to Why times you to the exit awhile. But it's more spirit you want, but x times seated Excellent boy minus warrants for

In this problem, we are learning how to use the technique of implicit differentiation. Now, when I learned this, I thought that this was very tricky to understand. So hopefully this problem helps you. And this video helps you understand a little bit more about how we use implicit differentiation. So where we start with this equation, eat the Y times sine X equals X plus X y. Now, just looking at this that looks like a really tricky, um equation to find the derivative of How would I do that if I have excess and wise? So the first thing that we're going to do by implicit differentiation is will take the derivative of each side of our equal sign. So we're basically saying that the derivative of E y sine X is equivalent to the derivative X plus X Y. So we'll take the derivative of each side. And when we do that, we'll get E to the Y times d y d x times Synnex plus e to the Y times a co sign of X equal to one plus one times y plus x times D Y d X. Now this is something that we can work with. We have to differentials d Y d X, and what we need is D Y dx by itself. So now every step we make is going to be is going to be in the goal to get d y dx by itself because that is our derivative, so we can do a little bit of simplification. Remember, we're trying to get do y dx by itself so we can subtract this year the y cosine X term. So once we do that, we'll get it to the Y times sine x times do I d x equal toe one plus Why minus e to the y close in x plus x times Do I d. X Now we can do a little bit of factoring to make this easier. We'll have eat the y minus sine x minus X times d Y d x equal toe one plus Why minus eat the y co sign X And now this is a very good position that we're in because this is an entire term times D Y d X, and we want the Dubai DX by itself. So we're just going to divide this term onto the other side to get you I d. X by itself. So we'll get do I d X equals one plus y minus e to the y co sign ex all over Eat the y sine X minus X and that is our derivative. So I hope that this problem helped you understand a little bit more about implicit differentiation, why we use it and how we can go through the process of using it. I know that it's a little bit tricky, but hopefully this made sense and you learn something from it.

And this problem. We are learning how to find the derivative of parametric equations. And this is going to come in handy when you're learning how to use Parametric curves and using calculus. Um, such as fighting the volume where the surface area of those curves so in parametric equations were given to functions of tea and we have to find d y d X. So how are we going to do that? Well, I hope that this problem helps you understand how we would. So we're given the function X equals t times e raised to the T. So what we can do first is we confined dx DT the derivative of that function while we would use power rule so we would have one times e to the t plus t times e to the t So we can simplify that to say DX DT equals one plus t times e to the t. And then we also have an equation for why? Why equals t plus the sine of t well again? We confined the derivative of that function d y d t. So we would find d y d t equals one plus the co sign of tea. Well, now you might be asking why Now I have to derivatives D x, t t and D y d t How do I find d y DX? We'll do y dx is equivalent to taking are equipped Pardon me, are derivative of y d Y d t divided by d x t t. So, essentially, we just take our derivative of y and put it as a numerator over that, Um, pardon me, the derivative of our function X. So we would get one plus co sign of tea over one plus t times e to the T. And that is our, um, derivative for the Parametric equations. Hope this helps you understand a little bit more about parametric equations and how we can find the derivative given to functions for X and Y.


Similar Solved Questions

5 answers
Sel Lhe Inliol-Ualue Prablem dy = axy+3xy dx
Sel Lhe Inliol-Ualue Prablem dy = axy+3xy dx...
5 answers
Identify the curve, sketch it and label all its properties: x2 -4x-8y =4
Identify the curve, sketch it and label all its properties: x2 -4x-8y =4...
5 answers
Consider following table for an unknown function f (x)f(x) 4 f(x) 4? f(x) 4? f(x)194 83 2831% 56 " 16(a ) use above table to find f(x) in terms of combinatorials(b ) what is value of function when x = 10(c) what is sum Zf(x)
Consider following table for an unknown function f (x) f(x) 4 f(x) 4? f(x) 4? f(x) 194 83 28 31 % 56 " 16 (a ) use above table to find f(x) in terms of combinatorials (b ) what is value of function when x = 10 (c) what is sum Zf(x)...
5 answers
Find the equation of the plane that is parallel to the 2-axis and makes an angle of 45 degrees with both the positive T-axis and the positive y-axis, Give the answer in vector-parametric [OTm
Find the equation of the plane that is parallel to the 2-axis and makes an angle of 45 degrees with both the positive T-axis and the positive y-axis, Give the answer in vector-parametric [OTm...
5 answers
WI) Write a polynomial function, f(x), with the following properties:a) of degree 6 b)with root of multiplicity 2 atx =-2 with root of multiplicity 3 atx=-1 d) with root of multiplicity 1 at x = 3 e) with Y-intercept of -4
w I) Write a polynomial function, f(x), with the following properties: a) of degree 6 b)with root of multiplicity 2 atx =-2 with root of multiplicity 3 atx=-1 d) with root of multiplicity 1 at x = 3 e) with Y-intercept of -4...
5 answers
Point) For each of the finite geometric series given below; indicate the number of terms in the sum and find the sum For the value of the sum,; enter an expression that gives the exact value; rather than entering an approximation. A 2+200.5) + 200.5)2 + 200.5)13 number of termsvalue of sumB.2(0.5)7 + 200.5)8 + 200.5)9 + +200.5)14 number of termsvalue of sum
point) For each of the finite geometric series given below; indicate the number of terms in the sum and find the sum For the value of the sum,; enter an expression that gives the exact value; rather than entering an approximation. A 2+200.5) + 200.5)2 + 200.5)13 number of terms value of sum B.2(0.5)...
5 answers
Given the two vectors A = (3.00ji (1.68)j and 6 = (-4.00)i (3.96)j, determine the following for the resultant vector R = 2A 3B_ (a) an expression of the vector in vector notationb) the magnitude of the vectorthe direction of the vector with respect to the x and axes counterclockwise from the +x axiscounterclockwise from the +Y axisTutorialShow My Work (Opbonal)
Given the two vectors A = (3.00ji (1.68)j and 6 = (-4.00)i (3.96)j, determine the following for the resultant vector R = 2A 3B_ (a) an expression of the vector in vector notation b) the magnitude of the vector the direction of the vector with respect to the x and axes counterclockwise from the +x ax...
1 answers
Early cameras were little more than a box with a pinhole on the side opposite the film. (a) What angular resolution would you expect from a pinhole with a $0.50-\mathrm{mm}$ diameter? (b) What is the greatest distance from the camera at which two point objects $15 \mathrm{cm}$ apart can be resolved? (Assume light with a wavelength of $520 \mathrm{nm} .$ )
Early cameras were little more than a box with a pinhole on the side opposite the film. (a) What angular resolution would you expect from a pinhole with a $0.50-\mathrm{mm}$ diameter? (b) What is the greatest distance from the camera at which two point objects $15 \mathrm{cm}$ apart can be resolved?...
1 answers
Write a differential formula that estimates the given change in volume or surface area. The change in the lateral surface area $S=2 \pi r h$ of a right circular cylinder when the height changes from $h_{0}$ to $h_{0}+d h$ and the radius does not change
Write a differential formula that estimates the given change in volume or surface area. The change in the lateral surface area $S=2 \pi r h$ of a right circular cylinder when the height changes from $h_{0}$ to $h_{0}+d h$ and the radius does not change...
4 answers
Consider the graduated cylinder above has been used to determine the volume of an object using displacement: The correct measurement for the volume of the metal object is:11.0 mL10.5 mL9.0 mL10.0 mL
Consider the graduated cylinder above has been used to determine the volume of an object using displacement: The correct measurement for the volume of the metal object is: 11.0 mL 10.5 mL 9.0 mL 10.0 mL...
5 answers
03: what is the main information we can obtain from the periodic tables regarding classification and different properties of materials? Discuss all these points in details?
03: what is the main information we can obtain from the periodic tables regarding classification and different properties of materials? Discuss all these points in details?...
5 answers
Oeromeiric FUNcTIONsUsing a trigonometric ratio to find a side length in a right triangleSolve for * in the triangle_ Round vour answer to the nearest tenth,
Oeromeiric FUNcTIONs Using a trigonometric ratio to find a side length in a right triangle Solve for * in the triangle_ Round vour answer to the nearest tenth,...
5 answers
Let &(5, 5) and b = = 5,3) _Find the angle between the vector; in degrees. (Round to the nearest hundredth_Let &(2, 3) and b = ( _ 1,k)_Find k so that & and b will be orthogonal (form 90 degree angle).
Let & (5, 5) and b = = 5,3) _ Find the angle between the vector; in degrees. (Round to the nearest hundredth_ Let & (2, 3) and b = ( _ 1,k)_ Find k so that & and b will be orthogonal (form 90 degree angle)....
1 answers
3. A school nurse wantS to determine it there is a signiicant relationship between the height and weight of students. The table below shows the height and weight given in cm and kg, respectively, of 10 students in a class.Test the hypothesis using 0.05 level of significance. Then, if possible, predict the estimated weight of a 180cm-tall student.
3. A school nurse wantS to determine it there is a signiicant relationship between the height and weight of students. The table below shows the height and weight given in cm and kg, respectively, of 10 students in a class. Test the hypothesis using 0.05 level of significance. Then, if possible, pred...
5 answers
19.A 0.10O m solution of which one of the following solutes will have the highest NaCl boiling . point? sucrose C; AI(CIO4)3 @AKCI04 Ca(C104)2
19.A 0.10O m solution of which one of the following solutes will have the highest NaCl boiling . point? sucrose C; AI(CIO4)3 @AKCI04 Ca(C104)2...
5 answers
J4 (4 Vnuy 5 ~CH; and CHz-CHz-Clz-CHz-NH; 'interaction would you expect between the following groups in the tertiary What type structure of protein? (0.25 pts) CH;and CH-CH;Ldoao banas helix of the secondary structure of a protein held together by 8. The parts of protein chain: (0.25 pts) Between two widely separated
J4 (4 Vnuy 5 ~CH; and CHz-CHz-Clz-CHz-NH; 'interaction would you expect between the following groups in the tertiary What type structure of protein? (0.25 pts) CH; and CH- CH; Ldoao banas helix of the secondary structure of a protein held together by 8. The parts of protein chain: (0.25 pts) B...

-- 0.022874--