15.4.8 problem 8

Internal problem ID [2921]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 8, page 34
Problem number : 8
Date solved : Monday, January 27, 2025 at 06:56:04 AM
CAS classification : [[_homogeneous, `class D`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \frac {2 y x -1}{y}+\frac {\left (x +3 y\right ) y^{\prime }}{y^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 20

dsolve((2*x*y(x)-1)/y(x)+(x+3*y(x))/y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {x}{3 \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {x^{2}}{3}} c_1 x}{3}\right )} \]

✓ Solution by Mathematica

Time used: 3.253 (sec). Leaf size: 37

DSolve[(2*x*y[x]-1)/y[x]+(x+3*y[x])/y[x]^2*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x}{3 W\left (\frac {1}{3} x e^{\frac {1}{3} \left (x^2-c_1\right )}\right )} \\ y(x)\to 0 \\ \end{align*}