35.5.13 problem 24

Internal problem ID [6147]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page 414
Problem number : 24
Date solved : Monday, January 27, 2025 at 01:38:27 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 37

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

\[ y = \left (c_2 \,{\mathrm e}^{\frac {3 x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_3 \,{\mathrm e}^{\frac {3 x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_1 \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 56

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

\[ y(x)\to e^{-x} \left (c_3 e^{3 x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_2 e^{3 x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+c_1\right ) \]