58.9.2 problem 2

Internal problem ID [14681]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page 124
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:50:10 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using reduction of order method given that one solution is

\begin{align*} y&=1+x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

\[ y = \left (x +1\right ) \left (c_1 \left (x +1\right )^{2}+c_2 \right ) \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to c_2 (x+1)^3+c_1 (x+1) \end{align*}

✓ Sympy. Time used: 0.151 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = C_{1} \left (x + 1\right )^{2} \]