9.24 problem 264

Internal problem ID [3520]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 9
Problem number: 264.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Riccati]

\[ \boxed {x^{2} y^{\prime }+x y \left (4+y x \right )=-2} \]

Solution by Maple

Time used: 0.0 (sec). Leaf size: 23

dsolve(x^2*diff(y(x),x)+2+x*y(x)*(4+x*y(x)) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {2 c_{1} -x}{x \left (c_{1} -x \right )} \]

Solution by Mathematica

Time used: 0.16 (sec). Leaf size: 26

DSolve[x^2 y'[x]+2 + x y[x](4+x y[x])==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {2}{x}+\frac {1}{x+c_1} y(x)\to -\frac {2}{x} \end{align*}