What is the solution for (dy)/(dx)=2sqrt(y+1)cos(x) ?

The solution for (dy)/(dx)=2sqrt(y+1)cos(x) is y=sin^2(x)+c_{1}sin(x)+(c_{1}^2)/4-1

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(dy)/(dx)=2sqrt(y+1)cos(x)

\frac{d y}{d x} = 2 y + 1 cos (x)

y = sin^{2} (x) + c_{1} sin (x) + \frac{c _{1}^{2}}{4} - 1

Solution steps

\frac{d y}{d x} = 2 y + 1 cos (x)

Solve separable ODE:

y = sin^{2} (x) + c_{1} sin (x) + \frac{c _{1}^{2}}{4} - 1

y = sin^{2} (x) + c_{1} sin (x) + \frac{c _{1}^{2}}{4} - 1

d er i v a t i v e 5 sec (7 x)

d er i v a t i v e ln (sin^{2} (x))

\frac{d y}{d x} = x + 2 x y

y^{^{''}} - 2 y^{^{'}} = (4 t + 9) sin (2 t)

\frac{d}{d x} (\frac{3}{2} sin (2 x))

What is the solution for (dy)/(dx)=2sqrt(y+1)cos(x) ?
The solution for (dy)/(dx)=2sqrt(y+1)cos(x) is y=sin^2(x)+c_{1}sin(x)+(c_{1}^2)/4-1