(d^4y)/(dx^4)+3(d^2y)/(dx^2)-4=0

解

\frac{d ^{4} y}{d x ^{4}} + 3 \frac{d ^{2} y}{d x ^{2}} - 4 = 0

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

解答ステップ

\frac{d ^{4} y}{d x ^{4}} + 3 \frac{d ^{2} y}{d x ^{2}} - 4 = 0

線形 ODE を解く:

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

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