73.17.35 problem 35

Internal problem ID [15498]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 35
Date solved : Monday, March 31, 2025 at 01:39:34 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 24

ode:=x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-9*y(x) = 3*x^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {35 c_1 \,x^{6}-12 x^{{7}/{2}}+35 c_2}{35 x^{3}} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 27

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

\[ y(x)\to c_2 x^3+\frac {c_1}{x^3}-\frac {12 \sqrt {x}}{35} \]

✓ Sympy. Time used: 0.248 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \frac {C_{1} + C_{2} x^{6} - \frac {12 x^{\frac {7}{2}}}{35}}{x^{3}} \]