29.16.14 problem 457

Internal problem ID [5055]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 457
Date solved : Monday, January 27, 2025 at 10:06:15 AM
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: 0.007 (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: 3.967 (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*}