83.26.10 problem 10

Internal problem ID [19263]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (C) at page 93
Problem number : 10
Date solved : Monday, March 31, 2025 at 07:03:43 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y&=x \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 21

ode:=x^2*diff(diff(y(x),x),x)+3*x*diff(y(x),x)-3*y(x) = x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 x +\frac {c_1}{x^{3}}+\frac {\ln \left (x \right ) x}{4}-\frac {x}{16} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 27

ode=x^2*D[y[x],{x,2}]+3*x*D[y[x],x]-3*y[x]==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_1}{x^3}+\frac {1}{4} x \log (x)+\left (-\frac {1}{16}+c_2\right ) x \]

✓ Sympy. Time used: 0.241 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 3*x*Derivative(y(x), x) - x - 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{3}} + C_{2} x + \frac {x \log {\left (x \right )}}{4} \]