y^{''}+y=\H(t)-\H(t-pi/2)

Lösung

y^{^{''}} + y = H (t) - H (t - \frac{π}{2})

y = c_{1} cos (t) + c_{2} sin (t) + cos (t) \cdot \int - sin (t) (H (t) - H (t - \frac{π}{2})) d t + sin (t) \cdot \int cos (t) (H (t) - H (t - \frac{π}{2})) d t

Schritte zur Lösung

y^{''} (t) + y = H (t) - H (t - \frac{π}{2})

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) + cos (t) \cdot \int - sin (t) (H (t) - H (t - \frac{π}{2})) d t + sin (t) \cdot \int cos (t) (H (t) - H (t - \frac{π}{2})) d t

y = c_{1} cos (t) + c_{2} sin (t) + cos (t) \cdot \int - sin (t) (H (t) - H (t - \frac{π}{2})) d t + sin (t) \cdot \int cos (t) (H (t) - H (t - \frac{π}{2})) d t

y^{^{''}} + 4 y^{^{'}} + 5 y = 25 x^{2} + 13 sin (2 x)

y^{^{''}} + 2 y^{^{'}} - 3 y = 4 e^{- 3 x} + 10 sin (x)

y^{^{''''}} + 2 y^{^{''}} + y = 9 t + 10

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

y^{^{''}} - 6 y^{^{'}} + 9 y = x + 1