how to solve it?

i was told to show first that x and e^x are a solution of some homogeneous equation

i got that it the homogeneous equation?

but the partivular solution is tough

y_p=(ax^2+bx+c)e^x

its hard to differentiate every time

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- Dec 8th 2010, 10:17 AMtransgalacticvariation problem

how to solve it?

i was told to show first that x and e^x are a solution of some homogeneous equation

i got that it the homogeneous equation?

but the partivular solution is tough

y_p=(ax^2+bx+c)e^x

its hard to differentiate every time - Dec 9th 2010, 09:53 AMTheEmptySet
Unfortunately you cannot use the method of undermined coefficients when the ODE does not have constant coefficients. You will need to use the variation of parameters.

Variation of parameters - Wikipedia, the free encyclopedia

since you are given the solutions to the homogeneous problem, we can solve for the particular solution.

1st. Put equation is standard form

2st. Assume solution of the form

3nd.Calculate the Wronskian

Now

and

Now

and

Now

Putting all of this together gives