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

Lösung

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

y = c_{1} + c_{2} cos (2 x) + c_{3} sin (2 x) + \frac{1}{8} sin^{2} (x) + \frac{1}{64} cos (4 x) cos (2 x) - \frac{1}{16} sin (2 x) (x - \frac{1}{4} sin (4 x))

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} cos (2 x) + c_{3} sin (2 x) + \frac{1}{8} sin^{2} (x) + \frac{1}{64} cos (4 x) cos (2 x) - \frac{1}{16} sin (2 x) (x - \frac{1}{4} sin (4 x))

y = c_{1} + c_{2} cos (2 x) + c_{3} sin (2 x) + \frac{1}{8} sin^{2} (x) + \frac{1}{64} cos (4 x) cos (2 x) - \frac{1}{16} sin (2 x) (x - \frac{1}{4} sin (4 x))

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

y^{^{''}} + 25 y = 9 sec (5 x)

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 4 y = e^{2 x}

y^{^{''}} + 9 y = g (t), y (0) = 2, y^{^{'}} (0) = 0

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