77y^{''''}+156y^{''}+64y=0

解答

77 y^{^{''''}} + 156 y^{^{''}} + 64 y = 0

y = c_{1} cos (\frac{2 t}{7}) + c_{2} sin (\frac{2 t}{7}) + c_{3} cos (\frac{4 t}{11}) + c_{4} sin (\frac{4 t}{11})

求解步骤

77 y^{(4)} (t) + 156 y^{''} (t) + 64 y = 0

求解线性方程:

y = c_{1} cos (\frac{2 t}{7}) + c_{2} sin (\frac{2 t}{7}) + c_{3} cos (\frac{4 t}{11}) + c_{4} sin (\frac{4 t}{11})

y = c_{1} cos (\frac{2 t}{7}) + c_{2} sin (\frac{2 t}{7}) + c_{3} cos (\frac{4 t}{11}) + c_{4} sin (\frac{4 t}{11})

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 2

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 9

y^{^{''}} - 4 y^{^{'}} - 21 y = 0, y (0) = a, y^{^{'}} (0) = 24

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

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