(y^')/x =y

Lösung

\frac{y ^{^{'}}}{x} = y

y = e^{\frac{x ^{2}}{2} + c_{1}}

Schritte zur Lösung

\frac{y ^{'} ( x )}{x} = y

Solve separable ODE:

y = e^{\frac{x ^{2}}{2} + c_{1}}

y = e^{\frac{x ^{2}}{2} + c_{1}}

(1 + x^{2}) y^{^{'}} + x e^{- y} = 0

x^{^{'}} = a x (1 - \frac{x}{c})

(x^{2} - 20 x + 75) y^{^{'}} = y

\frac{d y}{d x} = - \frac{7}{2} x^{4} y^{5}

2 x y (\frac{d y}{d x}) = 3