Internal problem ID [2676]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 41.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Riccati]
Solve \begin {gather*} \boxed {x^{2}+y+y^{2}-y^{\prime } x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve((x^2+y(x)+y(x)^2)-x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (x +c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.236 (sec). Leaf size: 12
DSolve[(x^2+y[x]+y[x]^2)-x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \tan (x+c_1) \\ \end{align*}