展开 (x-5)^2y''(x)+10(x-5)y'(x)+7y

解答

展开

(x - 5)^{2} y^{''} (x) + 10 (x - 5) y^{'} (x) + 7 y

x^{2} y'' (x) - 10 x y'' (x) + 25 y'' (x) + 10 x y' (x) - 50 y' (x) + 7 y

求解步骤

(x - 5)^{2} y^{''} (x) + 10 (x - 5) y^{'} (x) + 7 y

乘开

10 y^{'} (x) (x - 5) : 10 x y^{'} (x) - 50 y^{'} (x)

= (x - 5)^{2} y^{''} (x) + 10 x y^{'} (x) - 50 y^{'} (x) + 7 y

化简

(x - 5)^{2} y^{''} (x) + 10 x y^{'} (x) - 50 y^{'} (x) + 7 y : x^{2} y^{''} (x) - 10 x y^{''} (x) + 25 y^{''} (x) + 10 x y^{'} (x) - 50 y^{'} (x) + 7 y

= x^{2} y^{''} (x) - 10 x y^{''} (x) + 25 y^{''} (x) + 10 x y^{'} (x) - 50 y^{'} (x) + 7 y

e x p an d \frac{4 9 x ^{3}}{3 x}

e x p an d - 2 (x - 2 - 4 = - 3 (x - 5))

e x p an d \frac{4 y - y}{x y}

e x p an d \frac{4 x + 20}{( x + 2 ) ( x - 1 )}

e x p an d a \cdot (e^{b \cdot d} - b \cdot d - 1)