What is the solution for y^'=2sqrt(y+1)cos(x) ?

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

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y^'=2sqrt(y+1)cos(x)

y^{^{'}} = 2 y + 1 cos (x)

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

Solution steps

y^{'} (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

2 x d x - y d y = 0

\frac{d y}{d x} = \frac{20 x ^{4}}{y}, y > 0, x > 0

\frac{d y}{d x} = \frac{x ^{2} e ^{x^{3} - y^{2}}}{y}

\frac{d y}{d x} - x^{3} = x^{3} y

y^{^{'}} = \frac{5 x ^{2} - 1}{5 + 11 y}

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