67.14.16 problem 21.14 (b)

Internal problem ID [16713]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 21. Nonhomogeneous equations in general. Additional exercises page 391
Problem number : 21.14 (b)
Date solved : Thursday, October 02, 2025 at 01:38:02 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 18

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

\[ y = c_2 \,x^{2}+c_1 \,x^{3}+\frac {1}{2} x \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to c_2 x^3+c_1 x^2+\frac {x}{2} \end{align*}

✓ Sympy. Time used: 0.206 (sec). Leaf size: 15

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

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