64.10.5 problem 5

Internal problem ID [13411]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 05:41:59 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=0 \end{align*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 28

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

\[ y(x)\to c_1 e^{-x}+c_2 e^x+c_3 e^{3 x} \]