Internal problem ID [3076]
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]
\[ \boxed {{\mathrm e}^{2 x} y y^{\prime }=-2 x} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 16
dsolve([exp(2*x)*y(x)*diff(y(x),x)+2*x=0,y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {\left (2 x +1\right ) {\mathrm e}^{-2 x}} \]
✓ Solution by Mathematica
Time used: 1.816 (sec). Leaf size: 20
DSolve[{Exp[2*x]*y[x]*y'[x]+2*x==0,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {e^{-2 x} (2 x+1)} \]