y^'=2y,y(0)=3

Lösung

y^{^{'}} = 2 y, y (0) = 3

y = 3 e^{2 t}

Schritte zur Lösung

y^{'} (t) = 2 y

Solve separable ODE:

y = 3 e^{2 t}

y = 3 e^{2 t}

x d y = (y^{2} - 3 y + 2) d x

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

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

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

\frac{d y}{d x} = - 6 x^{2} y + 9 x^{2}