Internal problem ID [563]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.6. Page 100
Problem number: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_exponential_symmetries]]
Solve \begin {gather*} \boxed {y+\left (-{\mathrm e}^{-2 y}+2 y x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.049 (sec). Leaf size: 24
dsolve(y(x)+(-exp(-2*y(x))+2*x*y(x))*diff(y(x),x) = 0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left ({\mathrm e}^{-2 \,{\mathrm e}^{\textit {\_Z}}} c_{1}+\textit {\_Z} \,{\mathrm e}^{-2 \,{\mathrm e}^{\textit {\_Z}}}-x \right )} \]
✓ Solution by Mathematica
Time used: 0.275 (sec). Leaf size: 25
DSolve[y[x]+(-Exp[-2*y[x]]+2*x*y[x])*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=e^{-2 y(x)} \log (y(x))+c_1 e^{-2 y(x)},y(x)\right ] \]