The solution of the differential equation $x \sec y \frac{dy}{dx} = 1$ is

The general solution of $\sin ^{-1}\left(\frac{d y}{d x}\right)=x+y$ is

The solution of $\frac{dy}{dx} = \sqrt{1-y^2}$ with the initial condition $y(0) = 1$ is:

The solution of $y' = 1 + x + y^2 + xy^2$,$y(0) = 0$ is

The solution of the differential equation $\left( {1 + {e^{2y}}} \right){e^{{{\tan }^{ - 1}}x}}dx - \left( {1 + {x^2}} \right)\left( {{e^y} + {{\left( {{e^y} - 1} \right)}^2}} \right)dy = 0$ is

The general solution of $\frac{dy}{dx} = \cos^2(x-y-1)$ is given by $x=$