82.6.3 problem Ex. 3

Internal problem ID [18744]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 22
Problem number : Ex. 3
Date solved : Tuesday, January 28, 2025 at 12:14:09 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 60.022 (sec). Leaf size: 25

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

\[ y(x)\to -a W\left (-\frac {e^{\frac {c_1}{a}}}{a x^2}\right ) \]