y^{''}+3y^'+13y=52,y(0)=2,y^'(0)=1

Lösung

y^{^{''}} + 3 y^{^{'}} + 13 y = 52, y (0) = 2, y^{^{'}} (0) = 1

y = e^{- \frac{3 t}{2}} (- 2 cos (\frac{43 t}{2}) - \frac{4}{43} sin (\frac{43 t}{2})) + 4

Schritte zur Lösung

y^{''} (t) + 3 y^{'} (t) + 13 y = 52

Solve linear ODE:

y = e^{- \frac{3 t}{2}} (- 2 cos (\frac{43 t}{2}) - \frac{4}{43} sin (\frac{43 t}{2})) + 4

y = e^{- \frac{3 t}{2}} (- 2 cos (\frac{43 t}{2}) - \frac{4}{43} sin (\frac{43 t}{2})) + 4

y^{^{''}} + 2 y^{^{'}} - 3 y = 5 e^{2 x}, y (0) = 0, y^{^{'}} (0) = 5

y^{^{''}} + 3 y^{^{'}} + 2 y = 10 e^{x}

(d^{3} + 2 d^{2} - 5 d - 6) y = 6^{- 3} x

y^{^{''}} + 8 y^{^{'}} + 15 y = 10, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} - 36 y = 6 e^{2} x