19.3.12 problem 20

Internal problem ID [3555]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.8, page 68
Problem number : 20
Date solved : Monday, January 27, 2025 at 07:43:09 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 2 x \left (y+2 x \right ) y^{\prime }&=y \left (4 x -y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.284 (sec). Leaf size: 19

dsolve(2*x*(y(x)+2*x)*diff(y(x),x)=y(x)*(4*x-y(x)),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {2 x}{\operatorname {LambertW}\left (2 \,{\mathrm e}^{\frac {3 c_{1}}{2}} x^{{3}/{2}}\right )} \]

✓ Solution by Mathematica

Time used: 4.934 (sec). Leaf size: 29

DSolve[2*x*(y[x]+2*x)*D[y[x],x]==y[x]*(4*x-y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {2 x}{W\left (2 e^{-c_1} x^{3/2}\right )} \\ y(x)\to 0 \\ \end{align*}