y^{''}+y=\H(t)

Lösung

y^{^{''}} + y = H (t)

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

Schritte zur Lösung

y^{''} (t) + y = H (t)

Solve linear ODE:

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

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

y^{^{''}} - 2 y^{^{'}} + 5 y = 104 sin (3 x)

x^{^{''}} + 2 x^{^{'}} + 5 x = 4 t^{2}

y^{^{''}} - y^{^{'}} - 2 y = 1 - x

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 3 + 7 x

y^{^{''}} - y = \frac{e ^{2 x} - e ^{- 2 x}}{2}