64.22.2 problem 1 (b)

Internal problem ID [13588]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 11, The nth order homogeneous linear differential equation. Section 11.8, Exercises page 583
Problem number : 1 (b)
Date solved : Wednesday, March 05, 2025 at 10:04:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 t +1\right ) x^{\prime \prime }+t^{3} x^{\prime }+x&=0 \end{align*}

✗ Maple

ode:=(1+2*t)*diff(diff(x(t),t),t)+t^3*diff(x(t),t)+x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(2*t+1)*D[x[t],{t,2}]+t^3*D[x[t],t]+x[t]==0; 
ic={}; 
DSolve[{ode,ic},{x[t]},t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(t**3*Derivative(x(t), t) + (2*t + 1)*Derivative(x(t), (t, 2)) + x(t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

False