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# Solving ODE's with the method of variation of paramaters and reduction of order watch

1. hello, i was just wondering if anyone could help me with the following problem.

i calculated the wronskian as e^-4x and the general solution i obtained was y=c1e^-2x+c2xe^-2x-x+ln|x| but i'm not sure it is correct, any help would be appreciated
2. (Original post by Scary)
hello, i was just wondering if anyone could help me with the following problem.

i calculated the wronskian as e^-4x and the general solution i obtained was y=c1e^-2x+c2xe^-2x-x+ln|x| but i'm not sure it is correct, any help would be appreciated
Post a picture of your working, looks like you made a small slip somewhere.
3. (Original post by Zacken)
Post a picture of your working, looks like you made a small slip somewhere.
Excuse my atrocious handwriting
4. (Original post by Scary)
Excuse my atrocious handwriting
Yes, just a small slip - you've factored the characteristic equation incorrectly.

The wronskian will come out as
5. (Original post by Gregorius)
Yes, just a small slip - you've factored the characteristic equation incorrectly.

The wronskian will come out as
Ahh thank you!
6. So the final solution I acquired was y=Ae^2x+Bxe^2x+xe^2x(ln|x|-1) I'm just wondering when doing the intergration to calculate the particular integral should one include the constants of integration with the formula which you would use to generate this
7. bump

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