85.36.4 problem 1 (d)

Internal problem ID [22732]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 171
Problem number : 1 (d)
Date solved : Thursday, October 02, 2025 at 09:14:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-y&=1 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 28

ode:=x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)-y(x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{\frac {3}{2}+\frac {\sqrt {13}}{2}} c_2 +x^{\frac {3}{2}-\frac {\sqrt {13}}{2}} c_1 -1 \]

✗ Mathematica

ode=x**2*D[y[x],{x,2}]-2*x*D[y[x],{x,1}]-y[x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✓ Sympy. Time used: 0.327 (sec). Leaf size: 42

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

\[ y{\left (x \right )} = \frac {C_{1} + x^{- \frac {3}{2} + \frac {\sqrt {13}}{2}} \left (C_{2} x^{\frac {3}{2} + \frac {\sqrt {13}}{2}} - 1\right )}{x^{- \frac {3}{2} + \frac {\sqrt {13}}{2}}} \]