Solving differential equations with conditions

y’+ 2xy = 0; y= ce^(-x^2); y=0.5 when x = 0

I have to verify given function is a solution to differential equation. And Find C.

Help please!

Thank you.

Part (i) I guess you'll just have to find y'(x) that should be .

So y'(x) = .

now find 2yx. You know what y is, so that shouldn't be hard.

Add both and simplify to get 0.

This proves that the given function is a solution.

Part (ii) Next, use the given conditions, y=0.5 when x = 0.

Just plug the values for x and y in the given equation for y. That should be pretty easy