64.6.6 problem 6

Internal problem ID [13356]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 05:31:45 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 58

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

\begin{align*} y &= 0 \\ y &= \frac {\sqrt {2}\, \sqrt {-\left ({\mathrm e}^{2 x}-2\right ) c_{1}}}{{\mathrm e}^{2 x}-2} \\ y &= -\frac {\sqrt {2}\, \sqrt {-\left ({\mathrm e}^{2 x}-2\right ) c_{1}}}{{\mathrm e}^{2 x}-2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.092 (sec). Leaf size: 29

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

\begin{align*} y(x)\to 0 \\ y(x)\to \frac {c_1}{\sqrt {e^{2 x}-2}} \\ y(x)\to 0 \\ \end{align*}