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Beliebt Rechnen >

y^{''}-y=8e^{9t}+te^{9t}+5t^2e^{9t}

Lösung

y^{^{''}} - y = 8 e^{9 t} + t e^{9 t} + 5 t^{2} e^{9 t}

Lösung

y = c_{1} e^{t} + c_{2} e^{- t} + \frac{160 e ^{9 t} t ^{2} - 40 e ^{9 t} t + 261 e ^{9 t}}{2560}

Schritte zur Lösung

y^{''} (t) - y = 8 e^{9 t} + t e^{9 t} + 5 t^{2} e^{9 t}

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- t} + \frac{160 e ^{9 t} t ^{2} - 40 e ^{9 t} t + 261 e ^{9 t}}{2560}

y = c_{1} e^{t} + c_{2} e^{- t} + \frac{160 e ^{9 t} t ^{2} - 40 e ^{9 t} t + 261 e ^{9 t}}{2560}

Graph

Beliebte Beispiele

14y^{''}+y^'+y=x^2-4x

14 y^{^{''}} + y^{^{'}} + y = x^{2} - 4 x

y^{'''}-y^{''}=cos(2t)

y^{^{'''}} - y^{^{''}} = cos (2 t)

y^{''}-3y^'+2y=2xe^x

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

y^{''}-2y^'-3y=e^t,y(0)=2,y^'(0)=4

y^{^{''}} - 2 y^{^{'}} - 3 y = e^{t}, y (0) = 2, y^{^{'}} (0) = 4

y^{^{''}} - y = 2 t - 4