15.4.13 problem 14

Internal problem ID [2926]
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 : 14
Date solved : Monday, January 27, 2025 at 06:56:52 AM
CAS classification : [[_homogeneous, `class D`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 20

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

\[ y = -\frac {x}{2 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {x^{2}}{4}} c_1 x}{2}\right )} \]

✓ Solution by Mathematica

Time used: 3.548 (sec). Leaf size: 37

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

\begin{align*} y(x)\to -\frac {x}{2 W\left (-\frac {1}{2} x e^{\frac {1}{4} \left (x^2-2 c_1\right )}\right )} \\ y(x)\to 0 \\ \end{align*}