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

Lösung

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

y = c_{1} e^{t} + c_{2} e^{- t} + \frac{e ^{t} t ^{2} - e ^{t} t}{4} + \frac{1}{3} e^{2 t}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- t} + \frac{e ^{t} t ^{2} - e ^{t} t}{4} + \frac{1}{3} e^{2 t}

y = c_{1} e^{t} + c_{2} e^{- t} + \frac{e ^{t} t ^{2} - e ^{t} t}{4} + \frac{1}{3} e^{2 t}

d er i v a t i v e 2 t (3 t^{3} - 7)^{4}

x \to \infty lim (\frac{ln ( x )}{e ^{x}})

\frac{d}{d x} (\frac{4 2}{3} x^{\frac{3}{2}})

d er i v a t i v e \frac{4}{x ^{3}}

\frac{\partial}{\partial y} (y + x + 2)