85.64.9 problem 1 (i)

Internal problem ID [22876]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 213
Problem number : 1 (i)
Date solved : Thursday, October 02, 2025 at 09:16:06 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=\sqrt {x}+\frac {1}{\sqrt {x}} \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 23

ode:=x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-9*y(x) = x^(1/2)+1/x^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2}{x^{3}}+c_1 \,x^{3}-\frac {4 \left (x +1\right )}{35 \sqrt {x}} \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to c_2 x^3+\frac {c_1}{x^3}-\frac {4 (x+1)}{35 \sqrt {x}} \end{align*}

✓ Sympy. Time used: 0.189 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt(x) + x**2*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) - 9*y(x) - 1/sqrt(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{3}} + C_{2} x^{3} - \frac {4 \sqrt {x}}{35} - \frac {4}{35 \sqrt {x}} \]