x^3y^{'''}-x^2y^{''}+2xy^'-2y=x

解

x^{3} y^{^{'''}} - x^{2} y^{^{''}} + 2 x y^{^{'}} - 2 y = x

y = c_{1} x^{2} + c_{2} x + c_{3} ln (x) x + \frac{- x ln ^{2} ( x ) - 2 x ln ( x ) - x}{2}

解答ステップ

x^{3} y^{'''} (x) - x^{2} y^{''} (x) + 2 x y^{'} (x) - 2 y = x

線形 ODE を解く:

y = c_{1} x^{2} + c_{2} x + c_{3} ln (x) x + \frac{- x ln ^{2} ( x ) - 2 x ln ( x ) - x}{2}

y = c_{1} x^{2} + c_{2} x + c_{3} ln (x) x + \frac{- x ln ^{2} ( x ) - 2 x ln ( x ) - x}{2}