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Beliebt Rechnen >

y^{''}-8y^'+16y=t^{-5}e^{4t}

Lösung

y^{^{''}} - 8 y^{^{'}} + 16 y = t^{- 5} e^{4 t}

Lösung

y = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{e ^{4 t}}{12 t ^{3}}

Schritte zur Lösung

y^{''} (t) - 8 y^{'} (t) + 16 y = t^{- 5} e^{4 t}

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{e ^{4 t}}{12 t ^{3}}

y = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{e ^{4 t}}{12 t ^{3}}

Graph

Beliebte Beispiele

x^{''}+7x^'+12x=e^{2t}+cos(4t)

x^{^{''}} + 7 x^{^{'}} + 12 x = e^{2 t} + cos (4 t)

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

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

y^{''}-2y^'+y=-4e^x+3x^2

y^{^{''}} - 2 y^{^{'}} + y = - 4 e^{x} + 3 x^{2}

y^{''}+3y^'+4y=8x+2

y^{^{''}} + 3 y^{^{'}} + 4 y = 8 x + 2

(d^2+d)y=x^2+2x-3

(d^{2} + d) y = x^{2} + 2 x - 3