12.17.3 problem section 9.1, problem 5(b) 1

Internal problem ID [2109]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.1. Page 471
Problem number : section 9.1, problem 5(b) 1
Date solved : Monday, January 27, 2025 at 05:42:32 AM
CAS classification : [[_3rd_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 x y^{\prime }+6 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 18

dsolve([x^3*diff(y(x),x$3)-x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+6*y(x)=0,y(1) = 1, D(y)(1) = 0, (D@@2)(y)(1) = 0],y(x), singsol=all)
 

\[ y = -\frac {x^{3}}{2}+\frac {1}{2 x}+x^{2} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 23

DSolve[{x^3*D[y[x],{x,3}]-x^2*D[y[x],{x,2}]-2*x*D[y[x],x]+6*y[x]==0,{y[1]==1,Derivative[1][y][1]==0,Derivative[2][y][1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {x^3}{2}+x^2+\frac {1}{2 x} \]