y^'=5y+2

Lösung

y^{^{'}} = 5 y + 2

y = \frac{e ^{5 t + c_{1}}}{5} - \frac{2}{5}

Schritte zur Lösung

y^{'} (t) = 5 y + 2

Solve separable ODE:

y = \frac{e ^{5 t + c_{1}}}{5} - \frac{2}{5}

y = \frac{e ^{5 t + c_{1}}}{5} - \frac{2}{5}

(x^{2} + 1) d x + \frac{1}{y} d y = 0

10 x^{2} y + 2 x^{3} y^{^{'}} - 16 y = 0

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

\frac{d y}{d x} = \frac{y x + 3 x - y - 3}{x y - 2 x + 4 y - 8}

\frac{d y}{d x} = \frac{9 ( 1 + x )}{x y}