60.1.135 problem 136

Internal problem ID [10149]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 136
Date solved : Monday, January 27, 2025 at 06:30:03 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.149 (sec). Leaf size: 31

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