34.13.7 problem 27

Internal problem ID [8048]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 18. Linear equations with variable coefficients (Equations of second order). Supplemetary problems. Page 120
Problem number : 27
Date solved : Tuesday, September 30, 2025 at 05:14:43 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right )^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 20

ode:=4*x^2*diff(diff(y(x),x),x)+4*x^3*diff(y(x),x)+(x^2+1)^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {x^{2}}{4}} \sqrt {x}\, \left (\ln \left (x \right ) c_2 +c_1 \right ) \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 28

ode=4*x^2*D[y[x],{x,2}]+4*x^3*D[y[x],x]+(x^2+1)^2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-\frac {x^2}{4}} \sqrt {x} (c_2 \log (x)+c_1) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**3*Derivative(y(x), x) + 4*x**2*Derivative(y(x), (x, 2)) + (x**2 + 1)**2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False