29.9.17 problem 257

Internal problem ID [4857]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 257
Date solved : Monday, January 27, 2025 at 09:42:53 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.158 (sec). Leaf size: 31

DSolve[x^2 D[y[x],x]+x^2+x y[x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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