15.4.20 problem 21

Internal problem ID [2933]
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 : 21
Date solved : Monday, January 27, 2025 at 06:58:48 AM
CAS classification : [_exact]

\begin{align*} y \,{\mathrm e}^{y x}+2 y x +\left (x \,{\mathrm e}^{y x}+x^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

dsolve((y(x)*exp(x*y(x))+2*x*y(x))+(x*exp(x*y(x))+x^2)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.465 (sec). Leaf size: 28

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

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