29.7.10 problem 185

Internal problem ID [4785]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 185
Date solved : Tuesday, March 04, 2025 at 07:15:23 PM
CAS classification : [_Bernoulli]

\begin{align*} x y^{\prime }+\left (1-a y \ln \left (x \right )\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 15

ode:=x*diff(y(x),x)+(1-a*y(x)*ln(x))*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.166 (sec). Leaf size: 22

ode=x D[y[x],x]+(1-a y[x] Log[x])y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{a \log (x)+a+c_1 x} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.256 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + (-a*y(x)*log(x) + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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