(d+2d^2+1)y=cos(x)

解

(d + 2 d^{2} + 1) y = cos (x)

y = e^{- \frac{x}{4}} (c_{1} cos (\frac{7 x}{4}) + c_{2} sin (\frac{7 x}{4})) + \frac{1}{2} sin (x) - \frac{1}{2} cos (x)

解答ステップ

(d + 2 d^{2} + 1) y = cos (x)

線形 ODE を解く:

y = e^{- \frac{x}{4}} (c_{1} cos (\frac{7 x}{4}) + c_{2} sin (\frac{7 x}{4})) + \frac{1}{2} sin (x) - \frac{1}{2} cos (x)

y = e^{- \frac{x}{4}} (c_{1} cos (\frac{7 x}{4}) + c_{2} sin (\frac{7 x}{4})) + \frac{1}{2} sin (x) - \frac{1}{2} cos (x)