85.1.13 problem 5 (g)

Internal problem ID [22418]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 12
Problem number : 5 (g)
Date solved : Thursday, October 02, 2025 at 08:38:47 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y&=2 x^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=x^2*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-12*y(x) = 2*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,x^{3}+\frac {c_1}{x^{4}}-\frac {x^{2}}{3} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 25

ode=x^2*D[y[x],{x,2}]+2*x*D[y[x],{x,1}]-12*y[x]==2*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1}{x^4}+c_2 x^3-\frac {x^2}{3} \end{align*}

✓ Sympy. Time used: 0.146 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 2*x**2 + 2*x*Derivative(y(x), x) - 12*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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