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Beliebt Rechnen >

y^{''}-4y^'+4y=t^3

Lösung

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{3}

Lösung

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + \frac{t ^{3}}{4} + \frac{3 t ^{2}}{4} + \frac{9 t}{8} + \frac{3}{4}

Schritte zur Lösung

y^{''} (t) - 4 y^{'} (t) + 4 y = t^{3}

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + \frac{t ^{3}}{4} + \frac{3 t ^{2}}{4} + \frac{9 t}{8} + \frac{3}{4}

y = c_{1} e^{2 t} + c_{2} t e^{2 t} + \frac{t ^{3}}{4} + \frac{3 t ^{2}}{4} + \frac{9 t}{8} + \frac{3}{4}

Graph

Beliebte Beispiele

(d^2y)/(dx^2)-6(dy)/(dx)+9y=(x+1)e^x

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 9 y = (x + 1) e^{x}

y^{''}-4y^'+2y=5e^x

y^{^{''}} - 4 y^{^{'}} + 2 y = 5 e^{x}

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

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

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

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

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