y(dy)/(dx)=5x(y^2+5)^2

Lösung

y \frac{d y}{d x} = 5 x (y^{2} + 5)^{2}

y = \frac{- 1 - 25 x ^{2} - 10 c _{1}}{5 x ^{2} + 2 c _{1}}, y = - \frac{- 1 - 25 x ^{2} - 10 c _{1}}{5 x ^{2} + 2 c _{1}}

Schritte zur Lösung

y \frac{d y}{d x} = 5 x (y^{2} + 5)^{2}

Solve separable ODE:

y = \frac{- 1 - 25 x ^{2} - 10 c _{1}}{5 x ^{2} + 2 c _{1}}, y = - \frac{- 1 - 25 x ^{2} - 10 c _{1}}{5 x ^{2} + 2 c _{1}}

y = \frac{- 1 - 25 x ^{2} - 10 c _{1}}{5 x ^{2} + 2 c _{1}}, y = - \frac{- 1 - 25 x ^{2} - 10 c _{1}}{5 x ^{2} + 2 c _{1}}

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

y^{^{'}} + y = y (t e^{t^{2}} + 1)

\frac{d v}{d t} + 2 v = 0

e^{x} y y^{^{'}} = e^{- y} (1 + e^{- 2 x})

y^{^{'}} = 8 y - 10