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

Lösung

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

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{1}{6} sin (4 x) - \frac{1}{12} cos (4 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{1}{6} sin (4 x) - \frac{1}{12} cos (4 x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{1}{6} sin (4 x) - \frac{1}{12} cos (4 x)

2 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 3 y = e^{2 x}

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 5 e^{- t} + 2

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 5 e^{- t} + 4

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 5 e^{- t} + 6

y^{^{''}} + 7 y^{^{'}} + 6 y = 6 cos (5 t + 1.5708) H (t)