Internal problem ID [1464]
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 6(b).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+7 y^{\prime }-5 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 25
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+7*diff(y(x),x)-5*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{x} \sin \left (2 x \right )+c_{3} {\mathrm e}^{x} \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 26
DSolve[y'''[x]-3*y''[x]+7*y'[x]-5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (c_2 \cos (2 x)+c_1 \sin (2 x)+c_3) \\ \end{align*}