64.8.3 problem 2

Internal problem ID [13391]
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 113
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 08:24:50 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+x y^{\prime }+x^{2} y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 1.272 (sec). Leaf size: 5

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

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.085 (sec). Leaf size: 6

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

\[ y(x)\to 0 \]