25.1.25 problem 25

Internal problem ID [4237]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 25
Date solved : Monday, January 27, 2025 at 08:43:28 AM
CAS classification : [_separable]

\begin{align*} {\mathrm e}^{2 x} y y^{\prime }+2 x&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.105 (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: 1.807 (sec). Leaf size: 20

DSolve[{Exp[2*x]*y[x]*D[y[x],x]+2*x==0,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {e^{-2 x} (2 x+1)} \]