The given differential equation is: \(\frac{dy}{dx}=sin^{-1}x\) \(⇒dy=sin^{-1}xdx\) Integrating both sides,we get: \(∫dy=∫sin^{-1}xdx\) \(⇒y=∫(sin^{-1}x.1)dx\) \(⇒y=sin^{-1}x.∫(1)dx-∫[(\frac{d}{dx}(sin^{-1}x).∫(1)dx)]dx\) \(⇒y=sin^{-1}x.x-∫(\frac{1}{\sqrt{1-x^2}}.x)dx\) \(⇒y=xsin^{-1}x+∫\frac{-x}{\sqrt{1-x^2}}dx...(1)\) Let \(1-x^2=t.\) \(⇒\frac{d}{dx}(1-x^2)=\frac{dt}{dx}\) \(⇒-2x=\frac{dt}{dx}\) \(⇒xdx=\frac{-1}{2}dt\) Substituting this value in equation(1),we get: \(y=xsin^{-1}x+∫\frac{1}{2}\sqrt{t}dt\) \(⇒y=xsin^{-1}x+\frac{1}{2}.∫(t)-\frac{1}{2}dt\) \(⇒y=xsin^{-1}x+\sqrt{t}+C\) \(⇒y=xsin^{-1}x+\sqrt{1-x^2}+C\) This is the required general solution of the given differential equation.