Internal problem ID [6138]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS.
Page 9
Problem number: 7.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(2*diff(y(x),x$3)+diff(y(x),x$2)-5*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{3} {\mathrm e}^{3 x}+c_{1} {\mathrm e}^{\frac {5 x}{2}}+c_{2} \right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 30
DSolve[2*y'''[x]+y''[x]-5*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{x/2}+c_2 e^{-2 x}+c_3 e^x \]