81y^{''}+36y^'+40y=0,y(0)=6,y^'(0)=7

Lösung

81 y^{^{''}} + 36 y^{^{'}} + 40 y = 0, y (0) = 6, y^{^{'}} (0) = 7

y = e^{- \frac{2 t}{9}} (6 cos (\frac{2 t}{3}) + \frac{25}{2} sin (\frac{2 t}{3}))

Schritte zur Lösung

81 y^{''} (t) + 36 y^{'} (t) + 40 y = 0

Solve linear ODE:

y = e^{- \frac{2 t}{9}} (6 cos (\frac{2 t}{3}) + \frac{25}{2} sin (\frac{2 t}{3}))

y = e^{- \frac{2 t}{9}} (6 cos (\frac{2 t}{3}) + \frac{25}{2} sin (\frac{2 t}{3}))

2 y^{^{''}} + 5 y^{^{'}} = 0, y (0) = 0, y (2) = 1

y^{^{''}} - 2 y^{^{'}} - y = 0, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} + y^{^{'}} = 0, y (\frac{π}{3}) = 16, y^{^{'}} (\frac{π}{3}) = - 32

(10 d^{3} + d^{2} - 7 d + 2) y = 0

l in e a r y^{^{'''}} + 3 y^{^{''}} - 8 y^{^{'}} - 30 y = 0