y''+y=\H(t-0)-2\H(t-1)

Lösung

y^{^{''}} + y = H (t - 0) - 2 H (t - 1)

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

Schritte zur Lösung

y^{''} (t) + y = H (t - 0) - 2 H (t - 1)

Solve linear ODE:

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

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

y^{^{''}} + 4 y^{^{'}} + 3 y = 4.5 sin (2 t)

l in e a r x^{^{''}} + x^{^{'}} = 1 - 2 t + t^{2}

y^{^{''}} + 25 y = 7 x

y^{^{''}} + y^{^{'}} - 6 y = 20 e^{t}, y (0) = 0, y^{^{'}} (0) = 1

2 y^{^{''}} + 6 y^{^{'}} = 10 sin (7 t)