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(25,00 Puanlar) Which of the following differential equations has solutions of the given curve family % + cy? = 17 a)z?y' +y+ 1 = b)wy+ (1 _ :)y =0 cJoy cy = 1...

Question

(25,00 Puanlar) Which of the following differential equations has solutions of the given curve family % + cy? = 17 a)z?y' +y+ 1 = b)wy+ (1 _ :)y =0 cJoy cy = 1 d)zly+ (1 r)ya) 0 a) b) b} c) d) Bos birak<Onceki3/4Sonraki>KapatVSinavi Bitir

(25,00 Puanlar) Which of the following differential equations has solutions of the given curve family % + cy? = 17 a)z?y' +y+ 1 = b)wy+ (1 _ :)y =0 cJoy cy = 1 d)zly+ (1 r)y a) 0 a) b) b} c) d) Bos birak <Onceki 3/4 Sonraki> Kapat VSinavi Bitir



Answers

(a) Use a CAS to find the general solution of each differential equation. (b) Find the particular solution that satisfies the given boundary condition. (c) Graph the particular solution of each differential equation over the interval $[\pi / 2,5 \pi / 2]$ $$ \frac{d y}{d x}+\frac{3 y}{x}=\sin x ; \quad y(\pi)=0 $$

We were given a function and in part a were asked to find the differential. We're told that why is equal to X plus one over X minus one. Call this ffx. The next prime of X is equal to the bottom X minus one times the director for the top, which is one plus the top X plus one times the derivative. The bottom just one all over the bottom X minus one squared This simplifies to two X over X minus one squared and therefore the differential D Y is negative. Two. Sorry, that should be minus the top. So minus X plus one. And so we actually get negative to over X minus one squared and therefore the differential is negative. Two over X minus one squared times DX then in part B, were given the values of X and DX and were asked to evaluate. De y called that X is equal to two that the exes five. It follows that D y from part A is negative. Two over tu minus one squared times five same as negative to over one squared is negative. Two times five, which is negative 0.1

Hello the level you are going to solve the problem number 44. For the first order linear differential equation. Ship of Bernales equations. Okay, so we have to get the general solution for the following the french equation. X. Dy mighty X plus two. Y equal. Bye. Sign X over X. Okay, so for number eight the by using case or C. S. So that or any device. So we can just get the general solution for that differential equations. So it will be y equal see at the constant -5 design X over X squared. And that's a general solution. Okay, for number B. Okay. For number B the particular solution that satisfies that boundary condition. Why? Oh boy equal zero is that's why you will be equal negative boy minus phi cuisine X over X squared. Okay, so we saw substitute would see equal. Bye. Okay. Okay, so for number see okay, we have to get the graph of the particular solution over the interval boy over to and five boy over to. So it will be as soon. Okay, so that's like half of the main uh that differential equation of the particular studios. Okay, Thanks for watching. And see you see you in the next differential equation. See you later.

Were given a function and in part a were asked to find the differential of this function. Function is why equals E to the X over tea? Sorry, x over 10. So we have. If we call this ffx, then F prime of X is equal to buy the chain rule 1/10 e to the X over 10 and therefore the differential d Y is equal to e to the X Over 10 over 10 DX in part B were given values of X and DX and we were asked to evaluate the differential for these values were given that X is equal to zero and the D X is equal to 0.1 then from part A, we had the differential de y is going to be 1/10 of E to the 0/10 times 0.1 and this is simplified 2.1

The institutions. We have to find the differential equation of the family of curl. That is why is equals two into into the power three X. Plus B. Into into the power five facts. And and we are the arbitrary constant. So I am going to differentiate the situation so different shoot with respect to X. And we get This is the way by DX is equals two 382 E. To the power three X. Plus. This is five B. Into into the power Fairfax. Let this is our equation 2nd. And this is the only question 1st. Now I'm going to differentiate it again. So this is the two white by the excess square as equals to nine into the part three X. Plus. This is 25 into B. To the power five X. That this is our equation third. Now I'm going to subject equation three minus aggression too. So this will comes out to be The two. Bye bye. The excess square minus. I'm going to multiply it with five also. So this will comes out to be five divided by D. X. S equals two minus six A. To the Power three X. Now from here we get the value of A. Into E. To the power three X. That is minus one by six. Into the to abide by D X squared minus five, divide by dx. No, similarly I am going to subject equation 3 -3 aggression. And this is multiplied by three. So this film comes out to be The two by by be excess where -3 into divide by DX. And this is then into mm sorry 10 B into the power five fax. From here we get the value of being too into the power five fax. That is one by 10 data. Wait by the exit square minus. Trying to divide by dx. Now for these values in equation one. So from the equation when we get this is why is equals two minus one by six into the two by by the X. is where Plus this is five x 16 to divide by the X. Plus one x 10 into day too. Bye bye. The axis where -3 x 10 into the Vibe, I the X. Now I can simplify this and this with me. The return is do you do right by the exit square -8 into divide by DX Plus 15 by equals to zero. So this is the require differential equation of the family of God. And this is our answer for the institution and for that option is the correct answer. Thank you.


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