20(d^4y)/(dx^4)+100(d^2y)/(dx^2)=139

解

20 \frac{d ^{4} y}{d x ^{4}} + 100 \frac{d ^{2} y}{d x ^{2}} = 139

y = c_{1} + c_{2} x + c_{3} cos (5 x) + c_{4} sin (5 x) + \frac{139 x ^{2}}{200}

解答ステップ

20 \frac{d ^{4} y}{d x ^{4}} + 100 \frac{d ^{2} y}{d x ^{2}} = 139

線形 ODE を解く:

y = c_{1} + c_{2} x + c_{3} cos (5 x) + c_{4} sin (5 x) + \frac{139 x ^{2}}{200}

y = c_{1} + c_{2} x + c_{3} cos (5 x) + c_{4} sin (5 x) + \frac{139 x ^{2}}{200}