83.26.3 problem 3

Internal problem ID [19256]
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 : 3
Date solved : Monday, March 31, 2025 at 07:03:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=x^{4} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 22

ode:=x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+4*y(x) = x^4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2}{x^{2}}+\frac {\ln \left (x \right ) c_1}{x^{2}}+\frac {x^{4}}{36} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 26

ode=x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+4*y[x]==x^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x^6+72 c_2 \log (x)+36 c_1}{36 x^2} \]

✓ Sympy. Time used: 0.338 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4 + x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + C_{2} \log {\left (x \right )} + \frac {x^{6}}{36}}{x^{2}} \]