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Beliebt Rechnen >

y^{''}-10y^'+25y=t^{-6}e^{5t}

Lösung

y^{^{''}} - 10 y^{^{'}} + 25 y = t^{- 6} e^{5 t}

Lösung

y = c_{1} e^{5 t} + c_{2} t e^{5 t} + \frac{e ^{5 t}}{20 t ^{4}}

Schritte zur Lösung

y^{''} (t) - 10 y^{'} (t) + 25 y = t^{- 6} e^{5 t}

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} t e^{5 t} + \frac{e ^{5 t}}{20 t ^{4}}

y = c_{1} e^{5 t} + c_{2} t e^{5 t} + \frac{e ^{5 t}}{20 t ^{4}}

Graph

Beliebte Beispiele

y^{''}-y^'-2y=xe^{4x}

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

q^{''}+100q^'+2500q=40,q(0)=0

q^{^{''}} + 100 q^{^{'}} + 2500 q = 40, q (0) = 0

(D^2+5)y=cos(sqrt(5))x

(D^{2} + 5) y = cos (5) x

3y^'+2y^{''}=-1000cos(3.14*t/(0.2))

3 y^{^{'}} + 2 y^{^{''}} = - 1000 cos (3.14 \cdot \frac{t}{0.2})

y^{''}-1/2 y^'-1=0,y(0)=100,y(3)=10

y^{^{''}} - \frac{1}{2} y^{^{'}} - 1 = 0, y (0) = 100, y (3) = 10