Internal problem ID [4407]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page
46
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y \,{\mathrm e}^{x +y}}{x^{2}+2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve(diff(y(x),x)=y(x)*exp(x+y(x))/(x^2+2),y(x), singsol=all)
\[ \frac {i \sqrt {2}\, {\mathrm e}^{i \sqrt {2}} \expIntegral \left (1, -x +i \sqrt {2}\right )}{4}-\frac {i \sqrt {2}\, {\mathrm e}^{-i \sqrt {2}} \expIntegral \left (1, -x -i \sqrt {2}\right )}{4}+\expIntegral \left (1, y \relax (x )\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 1.505 (sec). Leaf size: 81
DSolve[y'[x]==y[x]*Exp[x+y[x]]/(x^2+2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}[\text {Ei}(-\text {$\#$1})\&]\left [c_1-\frac {i e^{-i \sqrt {2}} \left (e^{2 i \sqrt {2}} \text {Ei}\left (x-i \sqrt {2}\right )-\text {Ei}\left (x+i \sqrt {2}\right )\right )}{2 \sqrt {2}}\right ] \\ y(x)\to 0 \\ \end{align*}