26.5.13 problem 17

Internal problem ID [4287]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, End of chapter, page 61
Problem number : 17
Date solved : Monday, January 27, 2025 at 08:48:35 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 16

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

\[ y \left (x \right ) = \frac {\operatorname {LambertW}\left (-x \left (\sin \left (x \right )+c_{1} \right )\right )}{x} \]

✓ Solution by Mathematica

Time used: 60.275 (sec). Leaf size: 19

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

\[ y(x)\to \frac {W(x (-\sin (x)+c_1))}{x} \]