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Beliebt Rechnen >

y^{''}-8y^'+16y=(7t^4-2t^3)e^{4t}

Lösung

y^{^{''}} - 8 y^{^{'}} + 16 y = (7 t^{4} - 2 t^{3}) e^{4 t}

Lösung

y = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{7 e ^{4 t} t ^{6}}{30} - \frac{e ^{4 t} t ^{5}}{10}

Schritte zur Lösung

y^{''} (t) - 8 y^{'} (t) + 16 y = (7 t^{4} - 2 t^{3}) e^{4 t}

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{7 e ^{4 t} t ^{6}}{30} - \frac{e ^{4 t} t ^{5}}{10}

y = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{7 e ^{4 t} t ^{6}}{30} - \frac{e ^{4 t} t ^{5}}{10}

Graph

Beliebte Beispiele

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

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

y^{''}-4y^'-5y=2e^{(3x)}

y^{^{''}} - 4 y^{^{'}} - 5 y = 2 e^{(3 x)}

y^{''}+5y^'+6y=19te^{5t}

y^{^{''}} + 5 y^{^{'}} + 6 y = 19 t e^{5 t}

y^{''}+2y^'+y=ln(x)

y^{^{''}} + 2 y^{^{'}} + y = ln (x)

y^{''}-12y^'+36y=5e^2x

y^{^{''}} - 12 y^{^{'}} + 36 y = 5 e^{2} x