y^{''}-2y^'+2y=e^2x(cos(x)-6sin(x))

Lösung

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{2} x (cos (x) - 6 sin (x))

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) - \frac{8 e ^{2} x sin ( x )}{5} - \frac{11 e ^{2} x cos ( x )}{5} + (- 12 e^{2} + \frac{274 e ^{2}}{25}) sin (x) - \frac{82 e ^{2}}{25} cos (x)

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + 2 y = e^{2} x (cos (x) - 6 sin (x))

Solve linear ODE:

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) - \frac{8 e ^{2} x sin ( x )}{5} - \frac{11 e ^{2} x cos ( x )}{5} + (- 12 e^{2} + \frac{274 e ^{2}}{25}) sin (x) - \frac{82 e ^{2}}{25} cos (x)

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) - \frac{8 e ^{2} x sin ( x )}{5} - \frac{11 e ^{2} x cos ( x )}{5} + (- 12 e^{2} + \frac{274 e ^{2}}{25}) sin (x) - \frac{82 e ^{2}}{25} cos (x)

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

y^{^{''}} - 9 y = e^{3 x}, y (0) = 3, y^{^{'}} (0) = 10

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