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Beliebt Rechnen >

y^{''}-10y^'+25y=t^{-9}e^{5t}

Lösung

y^{^{''}} - 10 y^{^{'}} + 25 y = t^{- 9} e^{5 t}

Lösung

y = c_{1} e^{5 t} + c_{2} t e^{5 t} + \frac{e ^{5 t}}{56 t ^{7}}

Schritte zur Lösung

y^{''} (t) - 10 y^{'} (t) + 25 y = t^{- 9} e^{5 t}

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} t e^{5 t} + \frac{e ^{5 t}}{56 t ^{7}}

y = c_{1} e^{5 t} + c_{2} t e^{5 t} + \frac{e ^{5 t}}{56 t ^{7}}

Graph

Beliebte Beispiele

y^{''}-14*y^{''}+45*y^'=32e^x

y^{^{''}} - 14 \cdot y^{^{''}} + 45 \cdot y^{^{'}} = 32 e^{x}

y^{''}-y^'-6y=4te^3t,y(0)=-5,y^'(0)=-3

y^{^{''}} - y^{^{'}} - 6 y = 4 t e^{3} t, y (0) = - 5, y^{^{'}} (0) = - 3

y^{''}+y^'-2y=-4,y(0)=2,y^'(0)=3

y^{^{''}} + y^{^{'}} - 2 y = - 4, y (0) = 2, y^{^{'}} (0) = 3

-y^{''}+y^'+2y=e^t

- y^{^{''}} + y^{^{'}} + 2 y = e^{t}

y^{''}-4y^'-21y=800e^{-t}

y^{^{''}} - 4 y^{^{'}} - 21 y = 800 e^{- t}