Internal problem ID [6112]
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]
\[ \boxed {y^{\prime } x -y-y^{2}=x^{2}} \]
✓ 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)
\[ y \left (x \right ) = \tan \left (x +c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.184 (sec). Leaf size: 12
DSolve[x*y'[x]==y[x]+x^2+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \tan (x+c_1) \]