x^2dy=(y^2-xy+x^2)dx

解

x^{2} d y = (y^{2} - x y + x^{2}) d x

y = - \frac{x}{ln ( x ) + c _{1}} + \frac{x ln ( x )}{ln ( x ) + c _{1}} + \frac{c _{1} x}{ln ( x ) + c _{1}}

解答ステップ

x^{2} d y = (y^{2} - x y + x^{2}) d x

置換を使用して解く:

y = - \frac{x}{ln ( x ) + c _{1}} + \frac{x ln ( x )}{ln ( x ) + c _{1}} + \frac{c _{1} x}{ln ( x ) + c _{1}}

y = - \frac{x}{ln ( x ) + c _{1}} + \frac{x ln ( x )}{ln ( x ) + c _{1}} + \frac{c _{1} x}{ln ( x ) + c _{1}}