48.4.15 problem Problem 3.22

Internal problem ID [7557]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page 218
Problem number : Problem 3.22
Date solved : Wednesday, March 05, 2025 at 04:45:31 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)-1/x^(1/2)*diff(y(x),x)+1/4/x^2*(x+x^(1/2)-8)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{\sqrt {x}} \left (c_{2} x^{3}+c_{1} \right )}{x} \]

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

ode=D[y[x],{x,2}]-1/x^(1/2)*D[y[x],x]+1/(4*x^2)*(x+x^(1/2)-8)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {e^{\sqrt {x}} \left (c_2 x^3+3 c_1\right )}{3 x} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) + (sqrt(x) + x - 8)*y(x)/(4*x**2) - Derivative(y(x), x)/sqrt(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -sqrt(x)*Derivative(y(x), (x, 2)) + Derivative(y(x), x) - y(x)/(4*x) - y(x)/(4*sqrt(x)) + 2*y(x)/x**(3/2) cannot be solved by the factorable group method