7.5.28 problem 28

Internal problem ID [132]
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 : 28
Date solved : Friday, February 07, 2025 at 07:56:08 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

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

\[ y = \ln \left (x^{2} \left ({\mathrm e}^{2 x}-c_1 \right )\right ) \]

✓ Solution by Mathematica

Time used: 4.408 (sec). Leaf size: 18

DSolve[x*Exp[y[x]]*D[y[x],x]==2*(Exp[y[x]]+x^3*Exp[2*x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \log \left (x^2 \left (e^{2 x}+c_1\right )\right ) \]