(D^2+1)y=sec(xtan(x))

Lösung

(D^{2} + 1) y = sec (x tan (x))

y = c_{1} cos (x) + c_{2} sin (x) + cos (x) \cdot \int - sin (x) sec (x tan (x)) d x + sin (x) \cdot \int cos (x) sec (x tan (x)) d x

Schritte zur Lösung

(D^{2} + 1) y = sec (x tan (x))

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + cos (x) \cdot \int - sin (x) sec (x tan (x)) d x + sin (x) \cdot \int cos (x) sec (x tan (x)) d x

y = c_{1} cos (x) + c_{2} sin (x) + cos (x) \cdot \int - sin (x) sec (x tan (x)) d x + sin (x) \cdot \int cos (x) sec (x tan (x)) d x

4 x^{^{''}} + k x = 8 sin (t)

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

31 y^{^{''}} + 800 y = 100 cos (4 t), y (0) = 0, y^{^{'}} (0) = 0

x^{^{''''}} + 2 x^{^{''}} + x = 4 t e^{t}

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