20.3.22 problem Problem 22

Internal problem ID [3631]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 22
Date solved : Sunday, March 30, 2025 at 01:55:02 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=diff(diff(y(x),x),x)+1/x*diff(y(x),x) = 9*x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 16

ode=D[y[x],{x,2}]+1/x*D[y[x],x]==9*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^3+c_1 \log (x)+c_2 \]

✓ Sympy. Time used: 0.181 (sec). Leaf size: 12

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

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