83.26.4 problem 4

Internal problem ID [19249]
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 : 4
Date solved : Thursday, March 13, 2025 at 02:04:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x^{4} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 20

ode:=x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+6*y(x) = x^4; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 25

ode=x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==x^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} x^2 \left (x^2+2 c_2 x+2 c_1\right ) \]

✓ Sympy. Time used: 0.323 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4 + x**2*Derivative(y(x), (x, 2)) - 4*x*Derivative(y(x), x) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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