15.10.12 problem 12

Internal problem ID [3099]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 18, page 82
Problem number : 12
Date solved : Monday, January 27, 2025 at 07:19:25 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 35

dsolve(diff(y(x),x$3)-8*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{2 x}+c_2 \,{\mathrm e}^{-x} \sin \left (\sqrt {3}\, x \right )+c_3 \,{\mathrm e}^{-x} \cos \left (\sqrt {3}\, x \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 42

DSolve[D[y[x],{x,3}]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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