75.15.10 problem 441

Internal problem ID [16961]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.2 Homogeneous differential equations with constant coefficients. Exercises page 121
Problem number : 441
Date solved : Tuesday, January 28, 2025 at 09:43:48 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)
 

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

✓ 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]
 

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