y^{''}+16y=9sec(4x)

Lösung

y^{^{''}} + 16 y = 9 sec (4 x)

y = c_{1} cos (4 x) + c_{2} sin (4 x) + \frac{9}{16} ln (cos (4 x)) cos (4 x) + \frac{9}{4} x sin (4 x)

Schritte zur Lösung

y^{''} (x) + 16 y = 9 sec (4 x)

Solve linear ODE:

y = c_{1} cos (4 x) + c_{2} sin (4 x) + \frac{9}{16} ln (cos (4 x)) cos (4 x) + \frac{9}{4} x sin (4 x)

y = c_{1} cos (4 x) + c_{2} sin (4 x) + \frac{9}{16} ln (cos (4 x)) cos (4 x) + \frac{9}{4} x sin (4 x)

y^{^{''}} - 3 y^{^{'}} + y = 8 x

2 t^{(4)} - y^{^{'''}} - 9 y^{^{''}} + 4 y^{^{'}} + 4 y = 0

y^{^{''}} + 6 y^{^{'}} + 5 y = 2 e^{x} + 10 e^{5 x}

y^{^{''}} - 3 y^{^{'}} + 2 y = sin (x), y (0) = 1, y^{^{'}} (0) = 2

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