Internal problem ID [11691]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 10, Two tricks for nonlinear equations. Exercises page 97
Problem number: 10.4 (i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Riccati]
\[ \boxed {y x +y^{2}-x^{2} y^{\prime }=-x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(x*y(x)+y(x)^2+x^2-x^2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\ln \left (x \right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.314 (sec). Leaf size: 13
DSolve[x*y[x]+y[x]^2+x^2-x^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \tan (\log (x)+c_1) \]