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

Lösung

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

y = - \frac{ln ( 2 arctan ( x ) - 2 x - c _{1} )}{2}

Schritte zur Lösung

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

Solve separable ODE:

y = - \frac{ln ( 2 arctan ( x ) - 2 x - c _{1} )}{2}

y = - \frac{ln ( 2 arctan ( x ) - 2 x - c _{1} )}{2}

y^{^{'}} = - 0.004 y + 50, y (0) = 0

y^{^{'}} = (x + 6) (y - 3), y (0) = 6

\frac{d x}{d y} = x^{6} - x

y^{^{'}} = \frac{x + 5}{y}

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