x(dy)/(dx)=(1-5y^2)/(3y)

Lösung

x \frac{d y}{d x} = \frac{1 - 5 y ^{2}}{3 y}

y = \frac{- c _{1} + x ^{\frac{10}{3}}}{5 x ^{\frac{10}{3}}}, y = - \frac{- c _{1} + x ^{\frac{10}{3}}}{5 x ^{\frac{10}{3}}}

Schritte zur Lösung

x \frac{d y}{d x} = \frac{1 - 5 y ^{2}}{3 y}

Solve separable ODE:

y = \frac{- c _{1} + x ^{\frac{10}{3}}}{5 x ^{\frac{10}{3}}}, y = - \frac{- c _{1} + x ^{\frac{10}{3}}}{5 x ^{\frac{10}{3}}}

y = \frac{- c _{1} + x ^{\frac{10}{3}}}{5 x ^{\frac{10}{3}}}, y = - \frac{- c _{1} + x ^{\frac{10}{3}}}{5 x ^{\frac{10}{3}}}

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

\frac{y d y}{d x} + 4 x^{2} + 6 x + 1 = 0

y^{^{'}} = e^{3 x - 4 y}, y (0) = 0

\frac{d y}{d x} + 9 x^{8} y = 0, y = 6 e^{- x^{9}}

e^{y} y^{^{'}} = 1, y (0) = ln (x + c)