Internal problem ID [11680]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {{\mathrm e}^{2 x} y^{2}+\left (y \,{\mathrm e}^{2 x}-2 y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\sqrt {2}\, \sqrt {-\left ({\mathrm e}^{2 x}-2\right ) c_{1}}}{{\mathrm e}^{2 x}-2} \\ y \left (x \right ) &= -\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: 0.071 (sec). Leaf size: 29
DSolve[(Exp[2*x]*y[x]^2)+(Exp[2*x]*y[x]-2*y[x])*y'[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*}