78.2.31 problem 10.a

Internal problem ID [20983]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 2, Second order ODEs. Problems section 2.6
Problem number : 10.a
Date solved : Thursday, October 02, 2025 at 07:01:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y&=3 x^{2} \end{align*}

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

ode:=x^2*diff(diff(y(x),x),x)+3*x*diff(y(x),x)-3*y(x) = 3*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 x +\frac {c_1}{x^{3}}+\frac {3 x^{2}}{5} \]

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

ode=x^2*D[y[x],{x,2}]+3*x*D[y[x],x]-3*y[x]==3*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1}{x^3}+\frac {3 x^2}{5}+c_2 x \end{align*}

✓ Sympy. Time used: 0.147 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 3*x**2 + 3*x*Derivative(y(x), x) - 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{3}} + C_{2} x + \frac {3 x^{2}}{5} \]