Internal problem ID [1572]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.4. Variation of
Parameters for Higher Order Equations. Page 503
Problem number: section 9.4, problem 3.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y-2 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve(x^3*diff(y(x),x$3)-3*x^2*diff(y(x),x$2)+6*x*diff(y(x),x)-6*y(x)=2*x,y(x), singsol=all)
\[ y \relax (x ) = x \ln \relax (x )+\frac {3 x}{2}+c_{3} x^{3}+x^{2} c_{2}+x c_{1} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 24
DSolve[x^3*y'''[x]-3*x^2*y''[x]+6*x*y'[x]-6*y[x]==2*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (\log (x)+x (c_3 x+c_2)+\frac {3}{2}+c_1\right ) \\ \end{align*}