83.26.21 problem 21

Internal problem ID [19274]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (C) at page 93
Problem number : 21
Date solved : Monday, March 31, 2025 at 07:05:17 PM
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: 0.002 (sec). Leaf size: 29

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);
 

\[ y = c_1 \left (x +\frac {5}{2}\right )^{2+\sqrt {2}}+c_2 \left (x +\frac {5}{2}\right )^{2-\sqrt {2}} \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 40

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]
 

\[ y(x)\to c_2 (2 x+5)^{2+\sqrt {2}}+c_1 (2 x+5)^{2-\sqrt {2}} \]

✗ 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