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Beliebt Rechnen >

y^{''}-4y^'+4y=t^3y^0

Lösung

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{3} y^{0}

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} y^{0}

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

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