(dy)/(dx)=((x^2+y))/(x^3)

解

\frac{d y}{d x} = \frac{( x ^{2} + y )}{x ^{3}}

y = - \frac{Ei ( \frac{1}{2 x ^{2}} )}{2 e ^{\frac{1}{2 x ^{2}}}} + \frac{c _{1}}{e ^{\frac{1}{2 x ^{2}}}}

解答ステップ

\frac{d y}{d x} = \frac{( x ^{2} + y )}{x ^{3}}

線形 ODE を解く:

y = - \frac{Ei ( \frac{1}{2 x ^{2}} )}{2 e ^{\frac{1}{2 x ^{2}}}} + \frac{c _{1}}{e ^{\frac{1}{2 x ^{2}}}}

y = - \frac{Ei ( \frac{1}{2 x ^{2}} )}{2 e ^{\frac{1}{2 x ^{2}}}} + \frac{c _{1}}{e ^{\frac{1}{2 x ^{2}}}}