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Beliebt Rechnen >

x^{''}-3x^'+2x=t^2e^t

Lösung

x^{^{''}} - 3 x^{^{'}} + 2 x = t^{2} e^{t}

Lösung

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

Schritte zur Lösung

x^{''} (t) - 3 x^{'} (t) + 2 x = t^{2} e^{t}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

(D^3-D)y=4e^{(-x)}+3e^2x

(D^{3} - D) y = 4 e^{(- x)} + 3 e^{2} x

y^{''}+36y=60sin(6t)

y^{^{''}} + 36 y = 60 sin (6 t)

(d^2x)/(dt^2)+2(dx)/(dt)+2x=2

\frac{d ^{2} x}{d t ^{2}} + 2 \frac{d x}{d t} + 2 x = 2

(d^2y)/(dx^2)+(dy)/(dx)-y=xsinh(x)

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - y = x sinh (x)

linear y^{''}+y=sin(x)

l in e a r y^{^{''}} + y = sin (x)