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
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