y^{''}+4y^'+13y=0,y^'(pi/2)=12

Lösung

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y^{^{'}} (\frac{π}{2}) = 12

y = e^{- 2 t} (\frac{cos ( 3 t ) ( 12 e ^{π} - 2 c _{2} )}{3} + c_{2} sin (3 t))

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 13 y = 0

Solve linear ODE:

y = e^{- 2 t} (\frac{cos ( 3 t ) ( 12 e ^{π} - 2 c _{2} )}{3} + c_{2} sin (3 t))

y = e^{- 2 t} (\frac{cos ( 3 t ) ( 12 e ^{π} - 2 c _{2} )}{3} + c_{2} sin (3 t))

y^{^{''}} + 6 y^{^{'}} + 2 y = 0, y (0) = 4, y^{^{'}} (0) = 0

100 y^{^{''}} - 140 y^{^{'}} + 74 y = 0, y (3) = 6, y^{^{'}} (3) = 5

y^{^{''}} - 26 y^{^{'}} + 233 y = 0

(D^{4} + 2 D^{2}) y = 0

y^{^{''}} + 6 y^{^{'}} + 3 y = 0, y (0) = 0, y^{^{'}} (0) = 1