y^{''}-4y^'+4y=t^2e^{2t}+e^{2t}

Lösung

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{2} e^{2 t} + e^{2 t}

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + \frac{e ^{2 t} t ^{4}}{12} + \frac{e ^{2 t} t ^{2}}{2}

Schritte zur Lösung

y^{''} (t) - 4 y^{'} (t) + 4 y = t^{2} e^{2 t} + e^{2 t}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + \frac{e ^{2 t} t ^{4}}{12} + \frac{e ^{2 t} t ^{2}}{2}

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + \frac{e ^{2 t} t ^{4}}{12} + \frac{e ^{2 t} t ^{2}}{2}

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

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = 2 sin (4 x)

y^{^{''}} + 5 y = 6 t^{2} - 9, y (0) = 0, y^{^{'}} (0) = - 3

y^{^{''}} - y^{^{'}} + y = x^{2} - 2

y^{^{''}} - 3 y^{^{'}} + 2 y = 5 x e^{2 x} + 10 sin (2 x)