10.5.21 problem 28

Internal problem ID [1213]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 28
Date solved : Monday, January 27, 2025 at 04:45:25 AM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

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

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 24

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

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (c_1 \,{\mathrm e}^{-2 \,{\mathrm e}^{\textit {\_Z}}}+\textit {\_Z} \,{\mathrm e}^{-2 \,{\mathrm e}^{\textit {\_Z}}}-x \right )} \]

✓ Solution by Mathematica

Time used: 0.254 (sec). Leaf size: 25

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

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