7.5.24 problem 24

Internal problem ID [128]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 24
Date solved : Friday, February 07, 2025 at 07:55:41 AM
CAS classification : [_Bernoulli]

\begin{align*} 2 x y^{\prime }+y^{3} {\mathrm e}^{-2 x}&=2 x y \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 47

dsolve(2*x*diff(y(x),x)+y(x)^3*exp(-2*x)=2*x*y(x),y(x), singsol=all)
 

\begin{align*} y &= \frac {\sqrt {\left (\ln \left (x \right )+c_1 \right ) {\mathrm e}^{2 x}}}{\ln \left (x \right )+c_1} \\ y &= \frac {\sqrt {\left (\ln \left (x \right )+c_1 \right ) {\mathrm e}^{2 x}}}{-c_1 -\ln \left (x \right )} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.357 (sec). Leaf size: 41

DSolve[2*x*D[y[x],x]+y[x]^3*Exp[-2*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*}