Internal problem ID [4051]
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 12.39, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]
\[ \boxed {\left (x^{2}-y\right ) y^{\prime }+x=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve((x^2-y(x))*diff(y(x),x)+x=0,y(x), singsol=all)
\[ y \left (x \right ) = x^{2}+\frac {\operatorname {LambertW}\left (4 c_{1} {\mathrm e}^{-2 x^{2}-1}\right )}{2}+\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 5.491 (sec). Leaf size: 40
DSolve[(x^2-y[x])*y'[x]+x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2+\frac {1}{2} \left (1+W\left (-e^{-2 x^2-1+c_1}\right )\right ) \\ y(x)\to x^2+\frac {1}{2} \\ \end{align*}