29.15.31 problem 439

Internal problem ID [5037]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 439
Date solved : Monday, January 27, 2025 at 10:05:09 AM
CAS classification : [[_homogeneous, `class D`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x -y\right ) y^{\prime }&=y \left (1+2 y x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.052 (sec). Leaf size: 18

dsolve((x-y(x))*diff(y(x),x) = (1+2*x*y(x))*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 4.773 (sec). Leaf size: 30

DSolve[(x-y[x])D[y[x],x]==(1+2 x y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x}{W\left (x \left (-e^{x^2-1-c_1}\right )\right )} \\ y(x)\to 0 \\ \end{align*}