36.2.24 problem 29

Internal problem ID [6317]
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
Date solved : Monday, January 27, 2025 at 01:56:18 PM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

\begin{align*} \left ({\mathrm e}^{4 y}+2 x \right ) y^{\prime }-1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 41

dsolve((exp(4*y(x)) + 2*x)*diff(y(x),x)-1=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {\ln \left (-c_{1} -\sqrt {c_{1}^{2}+2 x}\right )}{2} \\ y \left (x \right ) &= \frac {\ln \left (-c_{1} +\sqrt {c_{1}^{2}+2 x}\right )}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.180 (sec). Leaf size: 113

DSolve[(Exp[4*y[x]]+2*x)*D[y[x],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*}