Internal problem ID [102]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{3} {\mathrm e}^{-2 x}+2 y^{\prime } x -2 y x=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 44
dsolve(y(x)^3/exp(2*x)+2*x*diff(y(x),x) = 2*x*y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {\sqrt {\left (\ln \left (x \right )+c_{1} \right ) {\mathrm e}^{2 x}}}{\ln \left (x \right )+c_{1}} y \left (x \right ) = -\frac {\sqrt {\left (\ln \left (x \right )+c_{1} \right ) {\mathrm e}^{2 x}}}{\ln \left (x \right )+c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.342 (sec). Leaf size: 41
DSolve[y[x]^3/Exp[2*x]+2*x*y'[x] == 2*x*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^x}{\sqrt {\log (x)+c_1}} y(x)\to \frac {e^x}{\sqrt {\log (x)+c_1}} y(x)\to 0 \end{align*}