64.1.10 problem 4(b)

Internal problem ID [13255]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number : 4(b)
Date solved : Tuesday, January 28, 2025 at 05:13:18 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x$3)-2*diff(y(x),x$2)-4*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 27

DSolve[D[y[x],{x,3}]-2*D[y[x],{x,2}]-4*D[y[x],x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (e^{4 x} (c_3 x+c_2)+c_1\right ) \]