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

Lösung

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

y = c_{1} e^{2 x} + c_{2} - \frac{1}{40} sin (4 x) - \frac{1}{20} cos (4 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} - \frac{1}{40} sin (4 x) - \frac{1}{20} cos (4 x)

y = c_{1} e^{2 x} + c_{2} - \frac{1}{40} sin (4 x) - \frac{1}{20} cos (4 x)

4 y^{^{''}} - y = 12 + 6 x

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

y^{^{''}} - 3 y^{^{'}} = 8 e^{2 t} - 2 e^{- t}

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

y^{^{''}} - 4 y^{^{'}} = 8 e^{6 x} (x - 1)