Internal problem ID [1459]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _exact, _linear, _homogeneous]]
\[ \boxed {x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y=0} \] 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: 0.015 (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)
\[ y \left (x \right ) = x^{2}+\frac {1}{2 x}-\frac {x^{3}}{2} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 23
DSolve[{x^3*y'''[x]-x^2*y''[x]-2*x*y'[x]+6*y[x]==0,{y[1]==1,y'[1]==0,y''[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x^3}{2}+x^2+\frac {1}{2 x} \]