75.5.4 problem 103

Internal problem ID [16740]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 5. Homogeneous equations. Exercises page 44
Problem number : 103
Date solved : Tuesday, January 28, 2025 at 09:20:30 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

dsolve(x^2*diff(y(x),x)=y(x)^2-x*y(x)+x^2,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: 0.150 (sec). Leaf size: 25

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