y^{''}+8y+15=-18e^{-2t},y(0)=-6,y^'(0)=10

Lösung

y^{^{''}} + 8 y + 15 = - 18 e^{- 2 t}, y (0) = - 6, y^{^{'}} (0) = 10

y = - \frac{21 cos ( 2 ^{1 + \frac{1}{2}} t )}{8} + \frac{7 sin ( 2 ^{1 + \frac{1}{2}} t )}{2 2} - \frac{3}{2} e^{- 2 t} - \frac{15}{8}

Schritte zur Lösung

y^{''} (t) + 8 y + 15 = - 18 e^{- 2 t}

Solve linear ODE:

y = - \frac{21 cos ( 2 ^{1 + \frac{1}{2}} t )}{8} + \frac{7 sin ( 2 ^{1 + \frac{1}{2}} t )}{2 2} - \frac{3}{2} e^{- 2 t} - \frac{15}{8}

y = - \frac{21 cos ( 2 ^{1 + \frac{1}{2}} t )}{8} + \frac{7 sin ( 2 ^{1 + \frac{1}{2}} t )}{2 2} - \frac{3}{2} e^{- 2 t} - \frac{15}{8}

y^{^{''}} - 6 y^{^{'}} + 25 y = t^{2} + 2

y^{^{''}} + 2 y^{^{'}} + 5 y = e^{- t} cos (2 t)

y^{^{''}} + y = 5 e^{- 2 x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 9 y^{^{'}} + 18 y = 2050 e^{(2 t)} cos (10 t)

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