(dy}{dx}(2y)+\frac{(1+y^2))/x =1

解

\frac{d y}{d x} (2 y) + \frac{( 1 + y ^{2} )}{x} = 1

y = - 1 + \frac{x}{2} + \frac{c _{1}}{x}, y = - - 1 + \frac{x}{2} + \frac{c _{1}}{x}

解答ステップ

\frac{d y}{d x} (2 y) + \frac{( 1 + y ^{2} )}{x} = 1

ベルヌーイ ODE を解く:

y = - 1 + \frac{x}{2} + \frac{c _{1}}{x}, y = - - 1 + \frac{x}{2} + \frac{c _{1}}{x}

y = - 1 + \frac{x}{2} + \frac{c _{1}}{x}, y = - - 1 + \frac{x}{2} + \frac{c _{1}}{x}