Internal problem ID [5358]
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(h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {x y^{\prime }+y-y^{\prime } \sqrt {1-x^{2} y}=0} \end {gather*}
✗ Solution by Maple
dsolve(x*diff(y(x),x)+y(x)=diff(y(x),x)*sqrt(1-x^2*y(x)),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x*y'[x]+y[x]==y'[x]*Sqrt[1-x^2*y[x]],y[x],x,IncludeSingularSolutions -> True]
Not solved