78.6.14 problem 4 (a)

Internal problem ID [18182]
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 (a)
Date solved : Tuesday, January 28, 2025 at 11:37:23 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 23

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

\[ \frac {x y^{2}-{\mathrm e}^{y}-c_1}{y^{2}} = 0 \]

✓ Solution by Mathematica

Time used: 0.212 (sec). Leaf size: 22

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

\[ \text {Solve}\left [x=\frac {e^{y(x)}}{y(x)^2}+\frac {c_1}{y(x)^2},y(x)\right ] \]