40.3.20 problem 25 (e)

Internal problem ID [6624]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 25 (e)
Date solved : Monday, January 27, 2025 at 02:16:15 PM
CAS classification : [_linear]

\begin{align*} y-\ln \left (x \right )-x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 11

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

\[ y = c_1 x +\ln \left (x \right )+1 \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 13

DSolve[(y[x]-Log[x])-x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \log (x)+c_1 x+1 \]