6y^{''''}+77y^{''}+25y=0

Lösung

6 y^{^{''''}} + 77 y^{^{''}} + 25 y = 0

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

Schritte zur Lösung

6 y^{(4)} (t) + 77 y^{''} (t) + 25 y = 0

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = 2, y^{^{'}} (0) = - 6

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = 1

y^{^{''}} + 15 y^{^{'}} + 44 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (- 1) = 2, y^{^{'}} (- 1) = 5

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 8 y = 0