83.3.9 problem 9

Internal problem ID [19065]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (B) at page 9
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 12:50:05 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 22

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

\[ y \left (x \right ) = -\operatorname {LambertW}\left (-\frac {{\mathrm e}^{-1}}{c_{1} \left ({\mathrm e}^{x}+1\right )}\right )-1 \]

✓ Solution by Mathematica

Time used: 3.771 (sec). Leaf size: 32

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

\begin{align*} y(x)\to -1-W\left (-\frac {e^{-1-c_1}}{e^x+1}\right ) \\ y(x)\to -1 \\ \end{align*}