What is the solution for (dy)/(dx)=2sqrt(y+1)cos(x),y(pi)=0 ?

The solution for (dy)/(dx)=2sqrt(y+1)cos(x),y(pi)=0 is y=sin^2(x)+2sin(x)

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(dy)/(dx)=2sqrt(y+1)cos(x),y(pi)=0

\frac{d y}{d x} = 2 y + 1 cos (x), y (π) = 0

y = sin^{2} (x) + 2 sin (x)

Solution steps

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

Solve separable ODE:

y = sin^{2} (x) + 2 sin (x)

y = sin^{2} (x) + 2 sin (x)

\frac{d x}{d t} = k x

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

2 \frac{d y}{d x} = 3 x^{2} (y^{2} - 1)

\frac{d r ( θ )}{r ( θ )} = \frac{r ( θ ) d θ}{θ ^{2}}

(1 - y^{2}) + x (\frac{d y}{d x}) = 0

What is the solution for (dy)/(dx)=2sqrt(y+1)cos(x),y(pi)=0 ?
The solution for (dy)/(dx)=2sqrt(y+1)cos(x),y(pi)=0 is y=sin^2(x)+2sin(x)