23.1.5 problem 1(e)

Internal problem ID [4095]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 1(e)
Date solved : Monday, January 27, 2025 at 08:08:28 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.342 (sec). Leaf size: 21

DSolve[Exp[2*y[x]]+(1+x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{2} \log (2 (\log (x+1)-c_1)) \]