85.65.5 problem 6

Internal problem ID [22885]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. B Exercises at page 213
Problem number : 6
Date solved : Thursday, October 02, 2025 at 09:16:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 32

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

\[ y = \left (x +2\right )^{\frac {1}{2}+\frac {\sqrt {5}}{2}} c_2 +\left (x +2\right )^{-\frac {\sqrt {5}}{2}+\frac {1}{2}} c_1 -4 \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 45

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

\begin{align*} y(x)&\to c_1 (x+2)^{\frac {1}{2} \left (1+\sqrt {5}\right )}+c_2 (x+2)^{\frac {1}{2}-\frac {\sqrt {5}}{2}}-4 \end{align*}

✗ Sympy

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

NotImplementedError : solve: Cannot solve (x + 2)**2*Derivative(y(x), (x, 2)) - y(x) - 4