4y^{''}-6y^'+2y=24e^{-x}-10sin(x)

Lösung

4 y^{^{''}} - 6 y^{^{'}} + 2 y = 24 e^{- x} - 10 sin (x)

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

Schritte zur Lösung

4 y^{''} (x) - 6 y^{'} (x) + 2 y = 24 e^{- x} - 10 sin (x)

Solve linear ODE:

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

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

10 y^{^{''}} + 60 y^{^{'}} + 50 y = 5 e^{- x}

y^{^{''}} - 16 y^{^{'}} + 64 y = \frac{2 e ^{8 x}}{3 x}

y^{^{''}} + 2 y^{^{'}} + 3 y = cos (2 t)

y^{^{''}} + y = cos (x), y (0) = 1, y^{^{'}} (0) = - 1

y^{^{''}} + 5 y^{^{'}} + 4 y = 8