19.3.10 problem 18

Internal problem ID [3553]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.8, page 68
Problem number : 18
Date solved : Monday, January 27, 2025 at 07:43:00 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} x^{2} y^{\prime }&=y^{2}+3 y x +x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(x^2*diff(y(x),x)=y(x)^2+3*x*y(x)+x^2,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: 28

DSolve[x^2*D[y[x],x]==y[x]^2+3*x*y[x]+x^2,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*}