1/4 y^{''}+y^'+y=sin(x)

Lösung

\frac{1}{4} y^{^{''}} + y^{^{'}} + y = sin (x)

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{12}{25} sin (x) - \frac{16}{25} cos (x)

Schritte zur Lösung

\frac{1}{4} y^{''} (x) + y^{'} (x) + y = sin (x)

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{12}{25} sin (x) - \frac{16}{25} cos (x)

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{12}{25} sin (x) - \frac{16}{25} cos (x)