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

Lösung

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

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) - \frac{7 e ^{2} x sin ( x )}{5} - \frac{9 e ^{2} x cos ( x )}{5} + (- 10 e^{2} + \frac{226 e ^{2}}{25}) sin (x) - \frac{68 e ^{2}}{25} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) - \frac{7 e ^{2} x sin ( x )}{5} - \frac{9 e ^{2} x cos ( x )}{5} + (- 10 e^{2} + \frac{226 e ^{2}}{25}) sin (x) - \frac{68 e ^{2}}{25} cos (x)

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) - \frac{7 e ^{2} x sin ( x )}{5} - \frac{9 e ^{2} x cos ( x )}{5} + (- 10 e^{2} + \frac{226 e ^{2}}{25}) sin (x) - \frac{68 e ^{2}}{25} cos (x)

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = x e^{\frac{x}{2}}

4 x^{^{''}} - 2 x = 7

y^{^{''}} + 4 y^{^{'}} + 4 = \frac{e ^{- 2 x}}{x ^{3}}

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

y^{^{''}} + 17 y^{^{'}} + 72 y = 4 x e^{2 x}