What is the solution for y(dy)/(dx)=sin^2(x) ?

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

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y(dy)/(dx)=sin^2(x)

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

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

Solution steps

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

Solve separable ODE:

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

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

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

y y^{^{'}} + 3 y = 8

\frac{d x}{d t} = \frac{a}{x} + b, x (0) = 0

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

(e^{y} + 1)^{2} e^{- y} d x + (e^{x} + 1)^{4} e^{- x} d y = 0

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