Internal problem ID [14187]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {-\frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y}=-\frac {\sqrt {\ln \left (x \right )}}{x}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 24
dsolve(sqrt(ln(x))/x=exp(3/y(x))/y(x)*diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {3}{\operatorname {RootOf}\left (2 \ln \left (x \right )^{\frac {3}{2}}-3 \,\operatorname {expIntegral}_{1}\left (\textit {\_Z} \right )+3 c_{1} \right )} \]
✓ Solution by Mathematica
Time used: 0.425 (sec). Leaf size: 29
DSolve[Sqrt[Log[x]]/x==Exp[3/y[x]]/y[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \text {InverseFunction}\left [-\operatorname {ExpIntegralEi}\left (\frac {3}{\text {$\#$1}}\right )\&\right ]\left [\frac {2}{3} \log ^{\frac {3}{2}}(x)+c_1\right ] \]