29.9.24 problem 264

Internal problem ID [4864]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 264
Date solved : Monday, January 27, 2025 at 09:45:30 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} x^{2} y^{\prime }+2+x y \left (4+y x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.187 (sec). Leaf size: 26

DSolve[x^2 D[y[x],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*}