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1. Find & particular solution to y" _ 3y' + %y = Zer + 1....

Question

1. Find & particular solution to y" _ 3y' + %y = Zer + 1.

1. Find & particular solution to y" _ 3y' + %y = Zer + 1.



Answers

Solve each equation. $$\frac{1}{y}+1=\frac{3}{y}-\frac{1}{2 y}$$

This question asks us to solve the given equation. Negative one plus one is zero. So we now have you ever wise one. However, this is a problem because this would imply that zero equals want because zero divide by anything is gonna be zero. However, this is a full statement. Therefore, the answer to this question is no solution. We cannot reasonably solve this equation.

In this problem we have in the shell Fellow Differential Equation, which is given by white double prime last three y, is equal to zero. Why zero is a call to one on twice prime cedar. It's according to three. Now we can sec it so this to function in creation, a psychiatrist to decommission, which is given by a T Square plus threes. A call to Syria This in place two years ago. Two. Squared off three I with Plus Linus No, let's recall the Pura when we have the complex route off the guy sophistication. They know we know the solutions. The General Solutions can be reaching us e to depart al flicks now, unfortunately, in this case al physical to zero because there is no real part. So this is going to be one time. See one time school sine squared off three x plus c. Two. I'm sign off. Squire rode off three x So this is going to be our general solution. So let's right tone the Purim. If Alfa Plus minus I beata are the solutions off, take actress sticky creation than the solutions competitiveness. So why is the country to the poor? Al fix times C. One time school sign beat X plus C two times Sign off be dykes. So there's that urine we are using in this problem. So now we have Why zero is they called to one? And why Prime Seaver? Is he going to three? So let's go back. If I use the condition why zero is equal to one. So we see that this time goes away and call Sign zero. It's simply is a call to one. So this implies C one is equal to one. So let's stick the derivative off. This life we have like prime mix is going to be C one times the derivative off course sign. It's a negative sign. Squire rode off three x Times Square Load off three plus C two times the derivative off court sign Ixis simply co sign Squire rode off three ex, followed by Sky Road off three So now we have the condition that why prime zero? Is it going to three? So this in place, If I take exit sickle to zero in this situation, then I end up getting C two time squared off. Two years ago, the three the same place he, too is called the square root of three. So then the political a solution can breed in us. Why is he going to co sign Squared off? Three x plus squared off? Three Signed off. Skye wrote off three x. So that's the specific solution afford initial.

Hello, everyone. This given question. We have to find a solution for why devilish minus y dash minus 12 eyes Jill. The conditions surviving is equal to zero and whitish one is one like so now First real light dogs related question for the visually question. So I'll square minus. I'll minus 12 is sequestered judo. So we get the root says one plus minus under one minus one plus 48. They were about to It just it was too one plus minus under 49 by two. So the roots off the equations is our request to fall and all that goes to minus tree, right? So since the WUSA riel and distinct So the general form general solution for the differential equation is see when you to develop four legs plus Saito eight by minus three X like Well, differentiate this so either. Taxes four c 1, 84 decks minus three. Saito double minus three X. Right now we have their player initial conditions. That is why one is Jeez. Oh, why one is equals to see 1 18 above four, plus c do it about minus tree. And why this one? If they questo one which is equals to foresee when a to the power four minus three C two A. To develop my industry. Right From these two conditions, we have to find a C one and C two. So when we we can from these two equations we get saved with request toe minus even $82. 7 Like from the first equation, we get set to us minus C when he took about seven this week and substitute in the 2nd 2nd the equation. So we get force even eight at about four. Plus, do you see one? A. To the power four is it was the one. So we get the value of Stephen as aided by minus four by seven and see to us it minus eight to the power three by seven. Like so, these are the values of C one and C two will substitute these values in the general form off the solutions we get by access. One day 78 double four X minus four minus one by 70 to cover Today minus three x Right, So this is the final solution for the initial value problem.

Hello welcome to this lesson. In this lesson you will find the general solution for the first quarter differentiate question why prime minus two Y. Is called to one. So compared to a general form why prime glass P. Of X. Y. That is he called to care of X. Oh and here if you are comparing the P of X would become negative tube And care of ex would become one. Okay. All right okay. At this point we would introduce an integrating factor each of us that is recalled to the integral of P. F. X. Dx. So this is he called to Integral of -2 DX. Which is called to -2 X. Then we can write why us one over E. To the part H. Of X. Times the integral E. To the far east of X. Than time scale of X. The X. So we have weather is equal to one over. Eat the bar negative two X integral negative. Uh Eat the bar negative two X. Times one the X. Okay so this is the call to eat the bar two X. And if we differentiate if we integrate this we have negative for an on to E. To the negative two X. M. Plus the constant C. So why is he called true negative half At this time that will become one. So we have plus See then eat the part two x. Okay so this is the general solution of the differential equation times for a time this is the end of the lesson


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