Question

Find a general solution for y’=2x(1-y^2)^(1/2)

Answer 1

Answer:

Step-by-step explanation:

$\frac{dy}{dx} =2x\sqrt{1-y^2} \\separate~the~variables~and~integrate\\\\\int\limits {\frac{1}{\sqrt{1-y^2} } } \, dy =\int 2x~dx\\ sin^{-1}(y)=2\frac{x^2}{2} +c\\y=sin(x^2+c),where~c~is~an~arbitrary~constant.$