68.15.22 problem 22

Internal problem ID [17748]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 22
Date solved : Thursday, October 02, 2025 at 02:27:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=x^{3} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 20

ode:=x^2*diff(diff(y(x),x),x)-5*x*diff(y(x),x)+9*y(x) = x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{3} \left (c_2 +c_1 \ln \left (x \right )+\frac {\ln \left (x \right )^{2}}{2}\right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 27

ode=x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+9*y[x]==x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} x^3 \left (\log ^2(x)+6 c_2 \log (x)+2 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.171 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3 + x**2*Derivative(y(x), (x, 2)) - 5*x*Derivative(y(x), x) + 9*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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