y^{''}-5y^'+4y=2te^t,y(0)=1,y^'(0)=-4

Lösung

y^{^{''}} - 5 y^{^{'}} + 4 y = 2 t e^{t}, y (0) = 1, y^{^{'}} (0) = - 4

y = (1 - \frac{70}{27}) e^{4 t} + \frac{70}{27} e^{t} - \frac{e ^{t} t ^{2}}{3} - \frac{2 e ^{t} t}{9}

Schritte zur Lösung

y^{''} (t) - 5 y^{'} (t) + 4 y = 2 t e^{t}

Solve linear ODE:

y = (1 - \frac{70}{27}) e^{4 t} + \frac{70}{27} e^{t} - \frac{e ^{t} t ^{2}}{3} - \frac{2 e ^{t} t}{9}

y = (1 - \frac{70}{27}) e^{4 t} + \frac{70}{27} e^{t} - \frac{e ^{t} t ^{2}}{3} - \frac{2 e ^{t} t}{9}

\frac{d ^{2} y}{d x ^{2}} + 14 \frac{d y}{d x} + 49 y = 4 e^{3 x}

y^{^{''}} - 2 y^{^{'}} - 3 y = 12 e x - 12

y^{^{''}} - y^{^{'}} - 2 y = 26 sin (x) + 40 x cos (x)

y^{^{''}} + 4 y^{^{'}} = x

y^{^{''}} + 2 y^{^{'}} - 3 y = (x + 1) e^{x}