y^{''}-4y^'+29y=0,y(0)=4,y^'(0)=18

Lösung

y^{^{''}} - 4 y^{^{'}} + 29 y = 0, y (0) = 4, y^{^{'}} (0) = 18

y = e^{2 t} (4 cos (5 t) + 2 sin (5 t))

Schritte zur Lösung

y^{''} (t) - 4 y^{'} (t) + 29 y = 0

Solve linear ODE:

y = e^{2 t} (4 cos (5 t) + 2 sin (5 t))

y = e^{2 t} (4 cos (5 t) + 2 sin (5 t))

y^{^{''}} - 83 y^{^{'}} + α y = 0

y^{^{''}} + y = 0, y^{^{'}} (\frac{π}{4}) = 2, y^{^{'}} (0) = 1

y^{^{''}} + 0 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''}} + 2 y^{^{'}} - 15 y = 0, y (0) = 1

5 y^{^{''}} + 20 y = 0, y (\frac{π}{4}) = 10, y (0) = 15