9.1.4 problem problem 41

Internal problem ID [931]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.2, Higher-Order Linear Differential Equations. General solutions of Linear Equations. Page 288
Problem number : problem 41
Date solved : Thursday, March 13, 2025 at 03:53:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.062 (sec). Leaf size: 29

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

\[ y(x)\to \frac {c_1 e^{x+1}-2 c_2 (x+2)}{\sqrt {2 e}} \]

✗ Sympy

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

False