Internal problem ID [1462]
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).
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) = k_{0}, y^{\prime }\relax (1) = k_{1}, y^{\prime \prime }\relax (1) = k_{2}] \end {align*}
✓ Solution by Maple
Time used: 0.026 (sec). Leaf size: 42
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) = k__0, D(y)(1) = k__1, (D@@2)(y)(1) = k__2],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-6 k_{0}+3 k_{2}\right ) x^{4}+\left (12 k_{0}+4 k_{1}-4 k_{2}\right ) x^{3}+6 k_{0}-4 k_{1}+k_{2}}{12 x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 43
DSolve[{x^3*y'''[x]-x^2*y''[x]-2*x*y'[x]+6*y[x]==0,{y[1]==k0,y'[1]==k1,y''[1]==k2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4 x^3 (3 \text {k0}+\text {k1}-\text {k2})+3 x^4 (\text {k2}-2 \text {k0})+6 \text {k0}-4 \text {k1}+\text {k2}}{12 x} \\ \end{align*}