78.6.15 problem 4 (b)

Internal problem ID [18183]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 10 (Linear equations). Problems at page 82
Problem number : 4 (b)
Date solved : Tuesday, January 28, 2025 at 11:37:24 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y-x y^{\prime }&=y^{\prime } y^{2} {\mathrm e}^{y} \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 17

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

\[ -y \,{\mathrm e}^{y}-y c_1 +x = 0 \]

✓ Solution by Mathematica

Time used: 0.209 (sec). Leaf size: 18

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

\[ \text {Solve}\left [x=e^{y(x)} y(x)+c_1 y(x),y(x)\right ] \]