77.5.5 problem 5

Internal problem ID [20385]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (D) at page 16
Problem number : 5
Date solved : Thursday, October 02, 2025 at 05:49:45 PM
CAS classification : [_linear]

\begin{align*} x \ln \left (x \right ) y^{\prime }+y&=2 \ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=x*ln(x)*diff(y(x),x)+y(x) = 2*ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \ln \left (x \right )+\frac {c_1}{\ln \left (x \right )} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 15

ode=x*Log[x]*D[y[x],x]+y[x]==2*Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \log (x)+\frac {c_1}{\log (x)} \end{align*}

✓ Sympy. Time used: 0.159 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*log(x)*Derivative(y(x), x) + y(x) - 2*log(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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