y^{''}-8y^'+20y=200x^2-91xe^x

Lösung

y^{^{''}} - 8 y^{^{'}} + 20 y = 200 x^{2} - 91 x e^{x}

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 10 x^{2} + 8 x + \frac{11}{5} - 7 x e^{x} - \frac{42}{13} e^{x}

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) + 20 y = 200 x^{2} - 91 x e^{x}

Solve linear ODE:

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 10 x^{2} + 8 x + \frac{11}{5} - 7 x e^{x} - \frac{42}{13} e^{x}

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 10 x^{2} + 8 x + \frac{11}{5} - 7 x e^{x} - \frac{42}{13} e^{x}

x^{^{''}} + x = sin^{2} (t)

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

x^{^{''}} + 10 x^{^{'}} + 29 x = t e^{- t}

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

x^{^{''}} + 36 x = 33 cos (5 t)