(D^4+2D^3-3D^2)y=3e^{2x}+4sin(x)

Lösung

(D^{4} + 2 D^{3} - 3 D^{2}) y = 3 e^{2 x} + 4 sin (x)

y = c_{1} e^{x} + c_{2} e^{- 3 x} + c_{3} + c_{4} x + \frac{3}{20} e^{2 x} + \frac{4}{5} sin (x) + \frac{2}{5} cos (x)

Schritte zur Lösung

(D^{4} + 2 D^{3} - 3 D^{2}) y = 3 e^{2 x} + 4 sin (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 3 x} + c_{3} + c_{4} x + \frac{3}{20} e^{2 x} + \frac{4}{5} sin (x) + \frac{2}{5} cos (x)

y = c_{1} e^{x} + c_{2} e^{- 3 x} + c_{3} + c_{4} x + \frac{3}{20} e^{2 x} + \frac{4}{5} sin (x) + \frac{2}{5} cos (x)

y^{^{'''}} - 4 y^{^{''}} + y^{^{'}} + 6 y = 3 e^{4 t}

y^{^{''}} + 4 y = sin (t) - H (t - 2 π) sin (t - 2 π)

y^{^{''}} + y = sin (a t)

y^{^{''}} - 4 y^{^{'}} + 13 y = 24 e^{2 x} cos (3 x)

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