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Beliebt Rechnen >

y^{''}+5y=-180x^2e^{(5x)}

Lösung

y^{^{''}} + 5 y = - 180 x^{2} e^{(5 x)}

Lösung

y = c_{1} cos (5 x) + c_{2} sin (5 x) - 6 x^{2} e^{5 x} + 4 x e^{5 x} - \frac{14}{15} e^{5 x}

Schritte zur Lösung

y^{''} (x) + 5 y = - 180 x^{2} e^{(5 x)}

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) - 6 x^{2} e^{5 x} + 4 x e^{5 x} - \frac{14}{15} e^{5 x}

y = c_{1} cos (5 x) + c_{2} sin (5 x) - 6 x^{2} e^{5 x} + 4 x e^{5 x} - \frac{14}{15} e^{5 x}

Graph

Beliebte Beispiele

y^{''}-10y^'+21y=e^{7t}

y^{^{''}} - 10 y^{^{'}} + 21 y = e^{7 t}

y^{''}+7y^'+10=x

y^{^{''}} + 7 y^{^{'}} + 10 = x

y^{'''}-16y^'=te^{-4t}

y^{^{'''}} - 16 y^{^{'}} = t e^{- 4 t}

y^{''}+4y=t^2+6e^t,y(0)=0,y^'(0)=1

y^{^{''}} + 4 y = t^{2} + 6 e^{t}, y (0) = 0, y^{^{'}} (0) = 1

y^{''}+4y=t^2+6e^t,y(0)=0,y^'(0)=3

y^{^{''}} + 4 y = t^{2} + 6 e^{t}, y (0) = 0, y^{^{'}} (0) = 3