Internal problem ID [5359]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS.
Page 9
Problem number: 1(i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Riccati]
Solve \begin {gather*} \boxed {x y^{\prime }-y-x^{2}-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 10
dsolve(x*diff(y(x),x)=y(x)+x^2+y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (x +c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.305 (sec). Leaf size: 12
DSolve[x*y'[x]==y[x]+x^2+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \tan (x+c_1) \\ \end{align*}