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

Lösung

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

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{7}{170} e^{2 x} sin (x) + \frac{11}{170} e^{2 x} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{7}{170} e^{2 x} sin (x) + \frac{11}{170} e^{2 x} cos (x)

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{7}{170} e^{2 x} sin (x) + \frac{11}{170} e^{2 x} cos (x)

y^{^{''}} - a y = - c

2 x^{^{''}} + 4 x^{^{'}} - 3 = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = sin (2 t), y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} + 5 y^{^{'}} + 6 y = e^{- 2 t}, y (0) = 0, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} - 16 \frac{d y}{d x} + 64 y = 7 e^{8 x}