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 : Wednesday, March 05, 2025 at 01:33:55 AM
CAS classification : [_linear]

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

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

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

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

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 13

ode=(y[x]-Log[x])-x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.236 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*Derivative(y(x), x) + y(x) - log(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x + \log {\left (x \right )} + 1 \]