23.3.6 problem 7(f)

Internal problem ID [4147]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 4. The general linear differential equation of order n. Exercises at page 63
Problem number : 7(f)
Date solved : Monday, January 27, 2025 at 08:40:01 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

dsolve(diff(y(x),x$3)+4*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} +\sin \left (2 x \right ) c_{2} +\cos \left (2 x \right ) c_3 \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 25

DSolve[D[y[x],{x,3}]+4*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{2} c_2 \cos (2 x)+c_1 \sin (x) \cos (x)+c_3 \]