Calculating Integral: Find Solutions to Differential Equation

[adichy]

Homework Statement

By making the change of variables x where x = sin \theta, calculate the indefinite
integral
\int \sqrt{1-x^2}
expressing you answer as a function of x.
Hence find the solution(s) to the differential equation
\frac{dy}{dx} \frac{d^2y}{dx^2} +x =0

Homework Equations

The Attempt at a Solution

so I've done the intergral and got

arc sin (x) /2 +(x(1-x^2)^1/2)/2+c

not sure how I am meant to use that to solve the differential, any advice would be apreciated.

edit: the latex comes ot completely wrong, dnt kno why..sorry :(

 

[adichy]

titled it wrong, can anyone tell me how to change it >.<

 

[hunt_mat]

Can you rewrite the equation using LaTeX? I don't quite get the equation...