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]]
\[ \boxed {x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }-2 y^{\prime } x +6 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = k_{0}, y^{\prime }\left (1\right ) = k_{1}, y^{\prime \prime }\left (1\right ) = k_{2}] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 40
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)
\[ y \left (x \right ) = \frac {3 \left (-2 k_{0} +k_{2} \right ) x^{4}+4 \left (k_{1} +3 k_{0} -k_{2} \right ) x^{3}+6 k_{0} -4 k_{1} +k_{2}}{12 x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 47
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]
\[ y(x)\to \frac {-6 \text {k0} \left (x^4-2 x^3-1\right )+4 \text {k1} \left (x^3-1\right )+3 \text {k2} x^4-4 \text {k2} x^3+\text {k2}}{12 x} \]