Let y = y(x) be the solution of the differential equation

${{dy} \over {dx}} = 2(y + 2\sin x - 5)x - 2\cos x$ such that y(0) = 7. Then y($\pi$) is equal to :

Let $x=x(y)$ be the solution of the differential equation $2(y+2) \log _{e}(y+2) d x+\left(x+4-2 \log _{e}(y+2)\right) d y=0, y-1$ with…

If $${{dy} \over {dx}} = {{{2^x}y + {2^y}{{.2}^x}} \over {{2^x} + {2^{x + y}}{{\log }_e}2}}$$, y(0) = 0, then for y = 1, the value of x…

Let y = y(x) be the solution of the differential equation $x(1 - {x^2}){{dy} \over {dx}} + (3{x^2}y - y - 4{x^3}) = 0$, $x 1$, with $y(2) =…

Let $y=y(x)$ be the solution curve of the differential equation $$\sin \left( {2{x^2}} \right){\log _e}\left( {\tan {x^2}} \right)dy +…

The general solution of the differential equation $\left(x-y^{2}\right) \mathrm{d} x+y\left(5 x+y^{2}\right) \mathrm{d} y=0$ is :