16(d^4y)/(dx^4)+24(d^2y)/(dx^2)+9y=0

解

16 \frac{d ^{4} y}{d x ^{4}} + 24 \frac{d ^{2} y}{d x ^{2}} + 9 y = 0

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

解答ステップ

16 \frac{d ^{4} y}{d x ^{4}} + 24 \frac{d ^{2} y}{d x ^{2}} + 9 y = 0

線形 ODE を解く:

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

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