Showing that x and 1+x² are solutions to this DE

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MuhTheKuh
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Hiya guys, I'm stuck on this new topic...
How do I show that x and 1+x² are both solutions to
(1-x²)*(d²y/dx²)+2x*(dy/dx)-2y=0
?

Thanks for your time
 
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A solution to a differential equation is one which, if you substitute it for y in your equation, you get zero on the left hand side like you're supposed to.

Can you substitute y=x and y=1+x2 into (1-x^2)\frac{d^2 y}{dx^2} + 2x \frac{dy}{dx} - 2y and see what you get?
 

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