23.3.470 problem 476

Internal problem ID [6184]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 476
Date solved : Tuesday, September 30, 2025 at 02:24:17 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} -\left (5+4 x \right ) y+32 x y^{\prime }+16 x^{2} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.041 (sec). Leaf size: 33

ode:=-(5+4*x)*y(x)+32*x*diff(y(x),x)+16*x^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{\sqrt {x}} c_1 \left (-1+\sqrt {x}\right )+{\mathrm e}^{-\sqrt {x}} c_2 \left (\sqrt {x}+1\right )}{x^{{5}/{4}}} \]

✓ Mathematica. Time used: 0.108 (sec). Leaf size: 51

ode=-((5 + 4*x)*y[x]) + 32*x*D[y[x],x] + 16*x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{-\sqrt {x}} \left (c_1 e^{2 \sqrt {x}} \left (\sqrt {x}-1\right )-c_2 \left (\sqrt {x}+1\right )\right )}{x^{5/4}} \end{align*}

✓ Sympy. Time used: 0.140 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*x**2*Derivative(y(x), (x, 2)) + 32*x*Derivative(y(x), x) + (-4*x - 5)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} J_{\frac {3}{2}}\left (i \sqrt {x}\right ) + C_{2} Y_{\frac {3}{2}}\left (i \sqrt {x}\right )}{\sqrt {x}} \]