展开 y(y'(x)-3y=x^2)

解答

展开

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

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

求解步骤

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

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

使用分配律:

a (b - c) = ab - a c

a = y, b = y^{'} (x), c = 3 y = x^{2}

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

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

乘开

y y^{'} (x) - 3 yy : y y^{'} (x) - 3 y^{2}

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

e x p an d 5 x - 3 (x + 2 = 15)

e x p an d \frac{8 ( 1 - 10 )}{9}

e x p an d \frac{( 2 + x ) ^{2}}{x}

e x p an d (x y + y^{2}) d x - (x^{2} + x y) d y

e x p an d - 3 (- 2 x - 4 v = 1)