(dy)/(dx)=(1-2y^2)/(ysin(x))

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

\frac{d y}{d x} = yy

y^{^{'}} + a \cdot y^{2} = 0

\frac{d y}{d x} = - \frac{4}{6} x^{3} y^{5}

\frac{d y}{d x} = (x^{3} y^{4})

4 x y^{2} d y = 2 y^{3} + 2 y d x