y^{''}+8y^'+20y=100x^2-26xe^x

Lösung

y^{^{''}} + 8 y^{^{'}} + 20 y = 100 x^{2} - 26 x e^{x}

y = e^{- 4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} - 4 x + \frac{11}{10} - \frac{26 e ^{x} x}{29} + \frac{260}{841} e^{x}

Schritte zur Lösung

y^{''} (x) + 8 y^{'} (x) + 20 y = 100 x^{2} - 26 x e^{x}

Solve linear ODE:

y = e^{- 4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} - 4 x + \frac{11}{10} - \frac{26 e ^{x} x}{29} + \frac{260}{841} e^{x}

y = e^{- 4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} - 4 x + \frac{11}{10} - \frac{26 e ^{x} x}{29} + \frac{260}{841} e^{x}

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

2 y^{^{''}} + y^{^{'}} + 4 y = x + 1

y^{^{''}} - y^{^{'}} - 6 y = 2 x

y^{^{''}} - y^{^{'}} - 6 y = 5 - 6^{x}, y (0) = 2, y^{^{'}} (0) = 4

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