y^{''}-6y^'+9y=12e^xsin(x)

Lösung

y^{^{''}} - 6 y^{^{'}} + 9 y = 12 e^{x} sin (x)

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{36}{25} e^{x} sin (x) + \frac{48}{25} e^{x} cos (x)

Schritte zur Lösung

y^{''} (x) - 6 y^{'} (x) + 9 y = 12 e^{x} sin (x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{36}{25} e^{x} sin (x) + \frac{48}{25} e^{x} cos (x)

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{36}{25} e^{x} sin (x) + \frac{48}{25} e^{x} cos (x)

y^{^{''}} + 6 y^{^{'}} + 9 y = \frac{e ^{- 3 x}}{x ^{2}}

2 y^{^{''}} + y^{^{'}} = 4 x, y (0) = 7, y^{^{'}} (0) = - 10

y^{^{''}} + 4 y = r (x)

y^{^{''}} - 2 y^{^{'}} + y = x^{3} + 5 x

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