xy(dy)/(dx)=y^2+xsqrt(4x^2+y^2)

解

x y \frac{d y}{d x} = y^{2} + x 4 x^{2} + y^{2}

y = ln^{2} (x) + 2 c_{1} ln (x) + c_{1}^{2} - 4 x, y = - x ln^{2} (x) + 2 c_{1} ln (x) + c_{1}^{2} - 4

解答ステップ

x y \frac{d y}{d x} = y^{2} + x 4 x^{2} + y^{2}

置換を使用して解く:

y = ln^{2} (x) + 2 c_{1} ln (x) + c_{1}^{2} - 4 x, y = - x ln^{2} (x) + 2 c_{1} ln (x) + c_{1}^{2} - 4

y = ln^{2} (x) + 2 c_{1} ln (x) + c_{1}^{2} - 4 x, y = - x ln^{2} (x) + 2 c_{1} ln (x) + c_{1}^{2} - 4