y^{''}+y=1-\H(t-3pi)

Lösung

y^{^{''}} + y = 1 - H (t - 3 π)

y = c_{1} cos (t) + c_{2} sin (t) + cos (t) \cdot \int - sin (t) (1 - H (t - 3 π)) d t + sin (t) \cdot \int cos (t) (1 - H (t - 3 π)) d t

Schritte zur Lösung

y^{''} (t) + y = 1 - H (t - 3 π)

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) + cos (t) \cdot \int - sin (t) (1 - H (t - 3 π)) d t + sin (t) \cdot \int cos (t) (1 - H (t - 3 π)) d t

y = c_{1} cos (t) + c_{2} sin (t) + cos (t) \cdot \int - sin (t) (1 - H (t - 3 π)) d t + sin (t) \cdot \int cos (t) (1 - H (t - 3 π)) d t

\frac{d ^{2} y}{d t ^{2}} + 4 y = 3 cos (2 t)

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

y^{^{''''}} - 8 y^{^{''}} + 16 y = 9 e^{2 x}

y^{^{''}} - 4 y = (x^{2} - 6) sin (2 x)

y^{^{''}} - y = - 6 sin (x), y (0) = 3, y^{^{'}} (0) = 2