The solution of $x^2 + y^2 \frac{dy}{dx} = 4$ is

If the solution of the differential equation $(2x+3y-2)dx+(4x+6y-7)dy=0$ with $y(0)=3$ is $\alpha x+\beta y+3 \log_e|2x+3y-\gamma|=6$,then $\alpha+2\beta+3\gamma$ is equal to

The general solution of the differential equation $\frac{dy}{dx} = \frac{xy+x-2y-2}{xy-2x+y-2}$ is

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

The solution of the differential equation $2x \frac{dy}{dx} - y = 0$,with the initial condition $y(1) = 2$,represents which of the following curves?

The general solution of the differential equation $\frac{dy}{dx} = e^{x+y}$ is . . . . . . .