Proof 1/(1+x²) is a solution of a differential equation

Question

Show that f(x)=1/(1+x²) is a solution to y"+4xy'+2y=0

Answer 1

Let y=f(x).
 
Take the first derivative of y, to get y'.
Take the derivative of y' to get y''.  This is also the second derivative.

 

Then substitute those derivatives, including the original function, into the equation and simplify.  If you get zero as a result, then you have a solution.