12.17.1 problem section 9.1, problem 2

Internal problem ID [2107]
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 2
Date solved : Monday, January 27, 2025 at 05:42:31 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 )&=-4\\ y^{\prime }\left (-1\right )&=-14\\ y^{\prime \prime }\left (-1\right )&=-20 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 20

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) = -4, D(y)(-1) = -14, (D@@2)(y)(-1) = -20],y(x), singsol=all)
 

\[ y = 3 x^{3}+\frac {25}{3 x}+\frac {22 x^{2}}{3} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 24

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]==-4,Derivative[1][y][-1]==-14,Derivative[2][y][-1]==-20}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {9 x^4+22 x^3+25}{3 x} \]