22y^{''''}+61y^{''}+25y=0

Lösung

22 y^{^{''''}} + 61 y^{^{''}} + 25 y = 0

y = c_{1} cos (\frac{t}{2}) + c_{2} sin (\frac{t}{2}) + c_{3} cos (\frac{5 t}{11}) + c_{4} sin (\frac{5 t}{11})

Schritte zur Lösung

22 y^{(4)} (t) + 61 y^{''} (t) + 25 y = 0

Solve linear ODE:

y = c_{1} cos (\frac{t}{2}) + c_{2} sin (\frac{t}{2}) + c_{3} cos (\frac{5 t}{11}) + c_{4} sin (\frac{5 t}{11})

y = c_{1} cos (\frac{t}{2}) + c_{2} sin (\frac{t}{2}) + c_{3} cos (\frac{5 t}{11}) + c_{4} sin (\frac{5 t}{11})

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 2, y^{^{'}} (0) = 5

- y^{^{''}} - π^{2} y = 0

y^{^{''}} + 20 y^{^{'}} + 100 y = 0, y (0) = 2, y^{^{'}} (0) = 1

\frac{d ^{2} v}{d x ^{2}} + k^{2} v = 0

4 \frac{d y}{d x} - \frac{d ^{2} y}{d x ^{2}} = 0