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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d x} = 6 x sec (y)

y^{^{'}} = - 6 x y, y (0) = 7

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

y^{^{'}} + x^{3} y = 0

\frac{d x}{d y} = \frac{6 x 5 - 2 x + 1}{cos ( y ) + ey}

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