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]]
\[ \boxed {x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y=2 x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
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)
\[ y \left (x \right ) = \frac {x \left (2 c_{3} x^{2}+2 c_{2} x +2 \ln \left (x \right )+2 c_{1} +3\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 25
DSolve[x^3*y'''[x]-3*x^2*y''[x]+6*x*y'[x]-6*y[x]==2*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \left (c_3 x^2+\log (x)+c_2 x+\frac {3}{2}+c_1\right ) \]