Internal problem ID [5616]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Section 2.7. HIGHER ORDER LINEAR EQUATIONS, COUPLED HARMONIC
OSCILLATORS Page 98
Problem number: 19(c).
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 }+2 x^{2} y^{\prime \prime }+x y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 18
dsolve(x^3*diff(y(x),x$3)+2*x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +\sin \left (\ln \relax (x )\right ) c_{2}+c_{3} \cos \left (\ln \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 22
DSolve[x^3*y'''[x]+2*x^2*y''[x]+x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3 x+c_1 \cos (\log (x))+c_2 \sin (\log (x)) \\ \end{align*}