29.18.33 problem 511

Internal problem ID [5107]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 511
Date solved : Monday, January 27, 2025 at 10:11:41 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 19

dsolve(x*y(x)*diff(y(x),x)+2*x^2-2*x*y(x)-y(x)^2 = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = x \left (1+\operatorname {LambertW}\left ({\mathrm e}^{2 c_{1} -1} x^{2}\right )\right ) \]

✓ Solution by Mathematica

Time used: 3.146 (sec). Leaf size: 25

DSolve[x y[x] D[y[x],x]+2 x^2-2 x y[x]-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x \left (1+W\left (e^{-1+c_1} x^2\right )\right ) \\ y(x)\to x \\ \end{align*}