y^{''}-5y=(x-1)sin(x)+(x+1)cos(x)

解

y^{^{''}} - 5 y = (x - 1) sin (x) + (x + 1) cos (x)

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} + \frac{2}{9} sin (x) - \frac{2}{9} cos (x) + \frac{- x sin ( x ) - x cos ( x )}{6}

解答ステップ

y^{''} (x) - 5 y = (x - 1) sin (x) + (x + 1) cos (x)

線形 ODE を解く:

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} + \frac{2}{9} sin (x) - \frac{2}{9} cos (x) + \frac{- x sin ( x ) - x cos ( x )}{6}

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} + \frac{2}{9} sin (x) - \frac{2}{9} cos (x) + \frac{- x sin ( x ) - x cos ( x )}{6}