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

Lösung

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

y = e^{- \frac{x}{4}} (c_{1} cos (\frac{7 x}{4}) + c_{2} sin (\frac{7 x}{4})) - \frac{1}{11} e^{2 x} + \frac{1}{22} e^{3 x}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- \frac{x}{4}} (c_{1} cos (\frac{7 x}{4}) + c_{2} sin (\frac{7 x}{4})) - \frac{1}{11} e^{2 x} + \frac{1}{22} e^{3 x}

y = e^{- \frac{x}{4}} (c_{1} cos (\frac{7 x}{4}) + c_{2} sin (\frac{7 x}{4})) - \frac{1}{11} e^{2 x} + \frac{1}{22} e^{3 x}

4 y^{^{''}} - 4 y^{^{'}} + y = 72 e^{\frac{t}{2}}

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

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = x e^{2 x}

(D - 3)^{2} y = e^{3 x}

y^{^{''}} - 8 y^{^{'}} + 16 y = - 5 e^{4 x} + \frac{e ^{4 x}}{x}