Internal problem ID [996]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Riccati]
\[ \boxed {y^{\prime } x^{2}-y x -y^{2}=x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 11
dsolve(x^2*diff(y(x),x)=x*y(x)+x^2+y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\ln \left (x \right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.174 (sec). Leaf size: 13
DSolve[x^2*y'[x]==x*y[x]+x^2+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \tan (\log (x)+c_1) \]