83.28.5 problem 5

Internal problem ID [19299]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (B) at page 106
Problem number : 5
Date solved : Monday, March 31, 2025 at 07:06:01 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=\frac {a}{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x) = a/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \ln \left (x \right ) a x +\left (-a +c_1 \right ) x +c_2 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 21

ode=D[y[x],{x,2}]==a/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -a x+a x \log (x)+c_2 x+c_1 \]

✓ Sympy. Time used: 0.149 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + a x \log {\left (x \right )} \]