76.38.1 problem Ex. 1

Internal problem ID [20216]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VII. Linear equations with variable coefficients. Problems at page 91
Problem number : Ex. 1
Date solved : Friday, October 03, 2025 at 07:38:09 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5-2 x \right ) y^{\prime }+8 y&=0 \end{align*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 51

ode:=(5+2*x)^2*diff(diff(y(x),x),x)-6*(5-2*x)*diff(y(x),x)+8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {30}{5+2 x}} \left (5+2 x \right )^{-1-i} \left (\operatorname {KummerU}\left (i, 1+2 i, \frac {30}{5+2 x}\right ) c_2 +\operatorname {KummerM}\left (i, 1+2 i, \frac {30}{5+2 x}\right ) c_1 \right ) \]

✓ Mathematica. Time used: 0.093 (sec). Leaf size: 95

ode=(5+2*x)^2*D[y[x],{x,2}]-6*(5-2*x)*D[y[x],x]+8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -(-1)^{-i} 30^{1-i} \left (\frac {1}{(2 x+5)^2}\right )^{\frac {1}{2}-\frac {i}{2}} \left (c_1 \operatorname {Hypergeometric1F1}\left (1-i,1-2 i,30 \sqrt {\frac {1}{(2 x+5)^2}}\right )+(-30)^{2 i} c_2 \left (\frac {1}{(2 x+5)^2}\right )^i \operatorname {Hypergeometric1F1}\left (1+i,1+2 i,30 \sqrt {\frac {1}{(2 x+5)^2}}\right )\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*x + 5)**2*Derivative(y(x), (x, 2)) + (12*x - 30)*Derivative(y(x), x) + 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False