展开 x^2y''(x)+xy'(x)+(x^2-1/4)y-x^{3/2}

解答

展开

x^{2} y^{''} (x) + x y^{'} (x) + (x^{2} - \frac{1}{4}) y - x^{\frac{3}{2}}

x^{2} y'' (x) + x y' (x) + x^{2} y - \frac{y}{4} - x^{\frac{3}{2}}

求解步骤

x^{2} y^{''} (x) + x y^{'} (x) + (x^{2} - \frac{1}{4}) y - x^{\frac{3}{2}}

乘开

y (x^{2} - \frac{1}{4}) : x^{2} y - \frac{y}{4}

= x^{2} y^{''} (x) + x y^{'} (x) + x^{2} y - \frac{y}{4} - x^{\frac{3}{2}}

e x p an d (t - a)^{2} + e^{- a t} - 2 cos (a t)

e x p an d ln (x) (x - 1)^{2}

e x p an d \frac{2}{5} y - \frac{3}{10} y

e x p an d (5 i, 3 j, 2 k) (- 4 i, - 1 j, - 5 k)

e x p an d \frac{1}{( s + 2 ) ( rcs + 1 )}