(d^4y)/(dx^4)+(d^2y)/(dx^2)=cos(4x)

解

\frac{d ^{4} y}{d x ^{4}} + \frac{d ^{2} y}{d x ^{2}} = cos (4 x)

y = c_{1} + c_{2} x + c_{3} cos (x) + c_{4} sin (x) + \frac{1}{240} cos (4 x)

解答ステップ

\frac{d ^{4} y}{d x ^{4}} + \frac{d ^{2} y}{d x ^{2}} = cos (4 x)

線形 ODE を解く:

y = c_{1} + c_{2} x + c_{3} cos (x) + c_{4} sin (x) + \frac{1}{240} cos (4 x)

y = c_{1} + c_{2} x + c_{3} cos (x) + c_{4} sin (x) + \frac{1}{240} cos (4 x)