21y^{''''}+82y^{''}+25y=0

Lösung

21 y^{^{''''}} + 82 y^{^{''}} + 25 y = 0

y = c_{1} cos (\frac{t}{3}) + c_{2} sin (\frac{t}{3}) + c_{3} cos (\frac{5 t}{7}) + c_{4} sin (\frac{5 t}{7})

Schritte zur Lösung

21 y^{(4)} (t) + 82 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}{7}) + c_{4} sin (\frac{5 t}{7})

y = c_{1} cos (\frac{t}{3}) + c_{2} sin (\frac{t}{3}) + c_{3} cos (\frac{5 t}{7}) + c_{4} sin (\frac{5 t}{7})

y^{^{''}} + 6 y^{^{'}} + 10 y = 0, y (0) = 0, y^{^{'}} (0) = 6

49 y^{^{''}} - 49 y = 0

\frac{d ^{2} y}{d x ^{2}} - 4 (\frac{d y}{d x}) - 32 y = 0

x^{^{''}} + 0.01 x^{^{'}} + x = 0

y^{^{''}} + 0 y^{^{'}} + 36 y = 0, y (0) = 4, y^{^{'}} (0) = 0