32.6.39 problem Exercise 12.39, page 103

Internal problem ID [5904]
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
Date solved : Monday, January 27, 2025 at 01:25:32 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]

\begin{align*} \left (x^{2}-y\right ) y^{\prime }+x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (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: 4.122 (sec). Leaf size: 40

DSolve[(x^2-y[x])*D[y[x],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*}