10.5.16 problem 21

Internal problem ID [1208]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 21
Date solved : Monday, January 27, 2025 at 04:45:15 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 34

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

\[ \frac {\left (-y^{2}+2 y-2\right ) {\mathrm e}^{y}+y^{2} x -c_1}{y^{2}} = 0 \]

✓ Solution by Mathematica

Time used: 0.239 (sec). Leaf size: 32

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

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