y^{''}-4y^'+4y=e^{2x}+cos(2x)

Lösung

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2 x} + cos (2 x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{2}}{2} - \frac{1}{8} sin (2 x)

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 4 y = e^{2 x} + cos (2 x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{2}}{2} - \frac{1}{8} sin (2 x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{e ^{2 x} x ^{2}}{2} - \frac{1}{8} sin (2 x)

y^{^{''}} + 4 x^{2} + 4 y = 6

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 8 y = x e^{x}

y^{^{''}} - 9 y^{^{'}} + 14 y = 12 - e^{x}

y^{^{''}} + 2 y^{^{'}} + 5 y = 45, y (0) = 2, y^{^{'}} (0) = 3

y^{^{''}} + y^{^{'}} - 20 y = e^{x} (82 + 84 x - 36 x^{2})