64.9.2 problem 2

Internal problem ID [13400]
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 : Tuesday, January 28, 2025 at 05:41:46 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*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve([(x+1)^2*diff(y(x),x$2)-3*(x+1)*diff(y(x),x)+3*y(x)=0,x+1],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 20

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

\[ y(x)\to c_2 (x+1)^3+c_1 (x+1) \]