y^{''}-y^'-2y=te^{2t}

Lösung

y^{^{''}} - y^{^{'}} - 2 y = t e^{2 t}

y = c_{1} e^{2 t} + c_{2} e^{- t} + \frac{e ^{2 t} t ^{2}}{6} - \frac{e ^{2 t} t}{9}

Schritte zur Lösung

y^{''} (t) - y^{'} (t) - 2 y = t e^{2 t}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- t} + \frac{e ^{2 t} t ^{2}}{6} - \frac{e ^{2 t} t}{9}

y = c_{1} e^{2 t} + c_{2} e^{- t} + \frac{e ^{2 t} t ^{2}}{6} - \frac{e ^{2 t} t}{9}

d er i v a t i v e - \frac{1}{9} (x^{- 9} - x^{18})

\frac{d}{d x} (3 x + 8)

t (\frac{d y}{d t}) = 2 t e^{t} - y + 6 t^{2}

\int_{0}^{2 π} sin^{2} (t) d t

\frac{\partial}{\partial x} (25 x^{(\frac{3}{4})} y^{\frac{1}{4}})