y^{''}-6y^'+9y=3e^{3x}+2sin(x)-cos(x)

Lösung

y^{^{''}} - 6 y^{^{'}} + 9 y = 3 e^{3 x} + 2 sin (x) - cos (x)

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{3 e ^{3 x} x ^{2}}{2} + \frac{11}{50} sin (x) + \frac{1}{25} cos (x)

Schritte zur Lösung

y^{''} (x) - 6 y^{'} (x) + 9 y = 3 e^{3 x} + 2 sin (x) - cos (x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{3 e ^{3 x} x ^{2}}{2} + \frac{11}{50} sin (x) + \frac{1}{25} cos (x)

y = c_{1} e^{3 x} + c_{2} x e^{3 x} + \frac{3 e ^{3 x} x ^{2}}{2} + \frac{11}{50} sin (x) + \frac{1}{25} cos (x)

2 y^{^{''}} + 2 y = - 16 cos (3 x)

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 3 e^{- t} + 2

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

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

y^{^{''}} + 4 y^{^{'}} + 4 y = x^{2} + 3