Internal problem ID [2567]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y \,{\mathrm e}^{2 x} y^{\prime }+2 x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.12 (sec). Leaf size: 16
dsolve([exp(2*x)*y(x)*diff(y(x),x)+2*x=0,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \sqrt {\left (1+2 x \right ) {\mathrm e}^{-2 x}} \]
✓ Solution by Mathematica
Time used: 0.199 (sec). Leaf size: 20
DSolve[{Exp[2*x]*y[x]*y'[x]+2*x==0,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {e^{-2 x} (2 x+1)} \\ \end{align*}