14.1.11 problem Problem 17

Internal problem ID [3568]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 17
Date solved : Tuesday, September 30, 2025 at 06:45:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=9 x^{2} \end{align*}

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

ode:=2*x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x) = 9*x^2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 23

ode=2*x^2*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==9*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.211 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) - 9*x**2 - x*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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