Internal problem ID [4046]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.33, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {\left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 50
dsolve((x^2*y(x)-1)*diff(y(x),x)+x*y(x)^2-1=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1+\sqrt {2 x^{3}-2 c_{1} x^{2}+1}}{x^{2}} \\ y \relax (x ) = -\frac {-1+\sqrt {2 x^{3}-2 c_{1} x^{2}+1}}{x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.764 (sec). Leaf size: 55
DSolve[(x^2*y[x]-1)*y'[x]+x*y[x]^2-1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1-\sqrt {1+x^2 (2 x+c_1)}}{x^2} \\ y(x)\to \frac {1+\sqrt {1+x^2 (2 x+c_1)}}{x^2} \\ \end{align*}