y^'=3xe^y

Lösung

y^{^{'}} = 3 x e^{y}

y = - ln (- \frac{3 x ^{2}}{2} - c_{1})

Schritte zur Lösung

y^{'} (x) = 3 x e^{y}

Solve separable ODE:

y = - ln (- \frac{3 x ^{2}}{2} - c_{1})

y = - ln (- \frac{3 x ^{2}}{2} - c_{1})

\frac{d y}{d x} = 10 x^{9} y

y^{^{'}} = x y^{3} (1 + x^{2})^{\frac{- 1}{2}}

\frac{x ^{2} + 2 x}{x + 1} y^{^{'}} - \frac{1}{y ^{3}} = 0

t^{2} \frac{d y}{d t} - t = 1 + y + t y, y (1) = 2

y^{^{'}} = 2 y (1 - \frac{y}{5})