25.1.24 problem 24

Internal problem ID [4236]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 24
Date solved : Monday, January 27, 2025 at 08:43:26 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 19

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

\[ y \left (x \right ) = -\ln \left (-\frac {1}{{\mathrm e}^{x^{2}} c_{1} -1}\right ) \]

✓ Solution by Mathematica

Time used: 2.001 (sec). Leaf size: 21

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

\begin{align*} y(x)\to \log \left (1+e^{x^2+c_1}\right ) \\ y(x)\to 0 \\ \end{align*}