83.41.10 problem 2 (ix)

Internal problem ID [19411]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise at end of chapter VIII. Page 141
Problem number : 2 (ix)
Date solved : Thursday, March 13, 2025 at 02:24:20 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=8 x^{3} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-y(x) = 8*x^3; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 19

ode=x^2*D[y[x],{x,2}]+x*D[y[x],x]-y[x]==8*x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^3+c_2 x+\frac {c_1}{x} \]

✓ Sympy. Time used: 0.207 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x**3 + x**2*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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