64.6.17 problem 17

Internal problem ID [13367]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 05:32:41 AM
CAS classification : [_exact, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.230 (sec). Leaf size: 24

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

\[ y = {\mathrm e}^{-2 x} \sqrt {2}\, \sqrt {{\mathrm e}^{2 x} \left (x^{2}+2\right )} \]

✓ Solution by Mathematica

Time used: 0.378 (sec). Leaf size: 25

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

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