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 $\displaystyle C * e^\frac {x^2} {2} * (-2x) $.
So y'(x) = $\displaystyle C * e^\frac {x^2} {2} * (-2x) $.
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