74.4.29 problem 29

Internal problem ID [15922]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 08:22:48 AM
CAS classification : [_separable]

\begin{align*} \frac {\sqrt {\ln \left (x \right )}}{x}&=\frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y} \end{align*}

✓ Solution by Maple

Time used: 0.051 (sec). Leaf size: 24

dsolve(sqrt(ln(x))/x=exp(3/y(x))/y(x)*diff(y(x),x),y(x), singsol=all)
 

\[ y = -\frac {3}{\operatorname {RootOf}\left (2 \ln \left (x \right )^{{3}/{2}}-3 \,\operatorname {Ei}_{1}\left (\textit {\_Z} \right )+3 c_{1} \right )} \]

✓ Solution by Mathematica

Time used: 0.463 (sec). Leaf size: 29

DSolve[Sqrt[Log[x]]/x==Exp[3/y[x]]/y[x]*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {InverseFunction}\left [-\operatorname {ExpIntegralEi}\left (\frac {3}{\text {$\#$1}}\right )\&\right ]\left [\frac {2}{3} \log ^{\frac {3}{2}}(x)+c_1\right ] \]