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

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

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

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

y = sin^{2} (x) + 2 c_{1} sin (x) + c_{1}^{2} - 1

Solution steps

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

Solve separable ODE:

y = sin^{2} (x) + 2 c_{1} sin (x) + c_{1}^{2} - 1

y = sin^{2} (x) + 2 c_{1} sin (x) + c_{1}^{2} - 1

y = e^{2 x^{2}}

\int (x + x e^{x}) d x

x \to 0 lim ((x^{2} + 1)^{\frac{1}{x}})

\int 5 x^{4} e^{9 x^{5}} d x

\frac{d}{d x} (\frac{1}{4} x^{3} + x - 1)

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