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

解

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

y = c_{1} e^{- x} + c_{2} x e^{- x} - \frac{1}{2} x - \frac{1}{2} x cos (2 x) + x cos^{2} (x) - \frac{3}{50} cos (2 x) + \frac{2}{25} sin (2 x) + \frac{1}{2}

解答ステップ

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

線形 ODE を解く:

y = c_{1} e^{- x} + c_{2} x e^{- x} - \frac{1}{2} x - \frac{1}{2} x cos (2 x) + x cos^{2} (x) - \frac{3}{50} cos (2 x) + \frac{2}{25} sin (2 x) + \frac{1}{2}

y = c_{1} e^{- x} + c_{2} x e^{- x} - \frac{1}{2} x - \frac{1}{2} x cos (2 x) + x cos^{2} (x) - \frac{3}{50} cos (2 x) + \frac{2}{25} sin (2 x) + \frac{1}{2}