y^{''}-5y^'-6y=2cos(3x)+4e^{2x}

Lösung

y^{^{''}} - 5 y^{^{'}} - 6 y = 2 cos (3 x) + 4 e^{2 x}

y = c_{1} e^{6 x} + c_{2} e^{- x} - \frac{1}{15} sin (3 x) - \frac{1}{15} cos (3 x) - \frac{1}{3} e^{2 x}

Schritte zur Lösung

y^{''} (x) - 5 y^{'} (x) - 6 y = 2 cos (3 x) + 4 e^{2 x}

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{- x} - \frac{1}{15} sin (3 x) - \frac{1}{15} cos (3 x) - \frac{1}{3} e^{2 x}

y = c_{1} e^{6 x} + c_{2} e^{- x} - \frac{1}{15} sin (3 x) - \frac{1}{15} cos (3 x) - \frac{1}{3} e^{2 x}

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

y^{^{''''}} + 4 y = cos (2 x)

y^{^{''}} + y^{^{'}} = sec (x) csc (x)

x^{^{''}} + x = cos (t)

y^{^{''}} + y^{^{'}} = t