19.1.10 problem 10

Internal problem ID [3524]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.4, page 36
Problem number : 10
Date solved : Tuesday, March 04, 2025 at 04:44:19 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {x^{2} y-32}{-x^{2}+16}+32 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 51

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

\[ y \left (x \right ) = \frac {-1440 \,{\mathrm e}^{-x -4} \left (x +4\right )^{2} \operatorname {Ei}_{1}\left (-x -4\right )+c_{1} \left (x +4\right )^{2} {\mathrm e}^{-x}+32 x^{2}-1696 x -7168}{\left (x -4\right )^{2}} \]

✓ Mathematica. Time used: 0.264 (sec). Leaf size: 56

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

\[ y(x)\to \frac {e^{-x-4} \left (1440 (x+4)^2 \operatorname {ExpIntegralEi}(x+4)+e^4 \left (32 e^x \left (x^2-53 x-224\right )+c_1 (x+4)^2\right )\right )}{(x-4)^2} \]

✗ Sympy

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

AssertionError : [False]