Internal problem ID [1461]
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) 3.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0, y^{\prime }\relax (1) = 0, y^{\prime \prime }\relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 21
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) = 0, D(y)(1) = 0, (D@@2)(y)(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {3 x^{4}-4 x^{3}+1}{12 x} \]
✓ 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]==0,y'[1]==0,y''[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(3 x-4) x^3+1}{12 x} \\ \end{align*}