44.5.9 problem 9

Internal problem ID [7071]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 9
Date solved : Monday, January 27, 2025 at 02:46:52 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 35

dsolve(y(x)*ln(x)*diff(y(x),x)=( (y(x)+1)/x)^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.393 (sec). Leaf size: 32

DSolve[y[x]*Log[x]*D[y[x],x]==( (y[x]+1)/x)^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {1}{\text {$\#$1}+1}+\log (\text {$\#$1}+1)\&\right ][\operatorname {ExpIntegralEi}(-\log (x))+c_1] \\ y(x)\to -1 \\ \end{align*}