Internal problem ID [4465]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page
54
Problem number: 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_exponential_symmetries]]
Solve \begin {gather*} \boxed {\left ({\mathrm e}^{4 y}+2 x \right ) y^{\prime }-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 41
dsolve((exp(4*y(x)) + 2*x)*diff(y(x),x)-1=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\ln \left (-c_{1}-\sqrt {c_{1}^{2}+2 x}\right )}{2} \\ y \relax (x ) = \frac {\ln \left (-c_{1}+\sqrt {c_{1}^{2}+2 x}\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.163 (sec). Leaf size: 113
DSolve[(Exp[4*y[x]]+2*x)*y'[x]-1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (-\sqrt {-\sqrt {2 x+c_1{}^2}-c_1}\right ) \\ y(x)\to \frac {1}{2} \log \left (-\sqrt {2 x+c_1{}^2}-c_1\right ) \\ y(x)\to \log \left (-\sqrt {\sqrt {2 x+c_1{}^2}-c_1}\right ) \\ y(x)\to \frac {1}{2} \log \left (\sqrt {2 x+c_1{}^2}-c_1\right ) \\ \end{align*}