Internal problem ID [1457]
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.
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 ) = -4, y^{\prime }\left (-1\right ) = -14, y^{\prime \prime }\left (-1\right ) = -20] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (x \right ) = \frac {22 x^{2}}{3}+\frac {25}{3 x}+3 x^{3} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 24
DSolve[{x^3*y'''[x]-x^2*y''[x]-2*x*y'[x]+6*y[x]==0,{y[-1]==-4,y'[-1]==-14,y''[-1]==-20}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {9 x^4+22 x^3+25}{3 x} \]