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

Lösung

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

y = e^{\frac{x}{2}} (c_{1} cos (\frac{19 x}{2}) + c_{2} sin (\frac{19 x}{2})) + \frac{1}{7} e^{2 x}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{\frac{x}{2}} (c_{1} cos (\frac{19 x}{2}) + c_{2} sin (\frac{19 x}{2})) + \frac{1}{7} e^{2 x}

y = e^{\frac{x}{2}} (c_{1} cos (\frac{19 x}{2}) + c_{2} sin (\frac{19 x}{2})) + \frac{1}{7} e^{2 x}

y^{^{''}} - 2 y^{^{'}} + y = 8 e^{x} - 5

\frac{d ^{2} y}{d x ^{2}} + 8 \frac{d y}{d x} + 16 y = 16 sin (x)

y^{^{''}} - 2 y^{^{'}} = 7 cos (3 t)

y^{^{''}} - 16 y^{^{'}} + 64 y = 504 sin (x) - 128 cos (x)

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