(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the ODE:

y''+p(x)y'+q(x)y=g(x)

It is given that the functions y=x[itex]^{2}[/itex], y=x and y[itex]\equiv[/itex]1

are solutions of the equation.

Find the general solution of the equation.

2. Relevant equations

3. The attempt at a solution

Well, given the three solutions, and taking into account that they are mutually linearly independent, I would say that any couple of these functions will give me a set that forms the general solution.

If i take y=x and y[itex]\equiv[/itex]1, I get the general solution:

y(x)=c1+c2*x

Now, I know that x[itex]^{2}[/itex] is also a solution, but it can't be derived from the general solution, so obviously I'm doing something wrong.

I also thought of the possibility that y=1 is a singular solution and the general solution is:

y(x)=c1*x+c2*x^2

does this makes sense?

This is a question from my midterm and i still can't figure it out. So... help?

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# Second order DE from my midtearm

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