(dy)/(dx)=sqrt(e^{-2ay)-1}

Lösung

\frac{d y}{d x} = e^{- 2 a y} - 1

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

Schritte zur Lösung

\frac{d y}{d x} = e^{- 2 a y} - 1

Solve separable ODE:

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

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

y^{^{'}} = y e^{t}, y (0) = 1

y^{^{'}} = 3 t^{2} \frac{y}{y + 1}, y (2) = 1

2 x y + 6 x + (x^{2} + 9) y^{^{'}} = 0

y y^{^{'}} = 2 x y + 2 x

\frac{d y}{d x} = - 4 e^{x + y}