1.91 problem 91

Internal problem ID [8428]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 91.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

\[ \boxed {x y^{\prime }-y=\frac {x}{\ln \left (x \right )}} \]

✓ Solution by Maple

Time used: 0.0 (sec). Leaf size: 11

dsolve(x*diff(y(x),x) - y(x) - x/ln(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 13

DSolve[x*y'[x] - y[x] - x/Log[x]==0,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to x (\log (\log (x))+c_1) \]