83.26.5 problem 5

Internal problem ID [19258]
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 : 5
Date solved : Monday, March 31, 2025 at 07:03:31 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y&=x^{4} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

ode:=x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)-4*y(x) = x^4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,x^{4}+\frac {x^{4} \ln \left (x \right )}{5}+\frac {c_1}{x} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 31

ode=x^2*D[y[x],{x,2}]-2*x*D[y[x],x]-4*y[x]==x^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{5} x^4 \log (x)+\left (-\frac {1}{25}+c_2\right ) x^4+\frac {c_1}{x} \]

✓ Sympy. Time used: 0.276 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4 + x**2*Derivative(y(x), (x, 2)) - 2*x*Derivative(y(x), x) - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + \frac {x^{5} \left (C_{2} + \log {\left (x \right )}\right )}{5}}{x} \]