64.10.17 problem 17

Internal problem ID [13423]
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 : 17
Date solved : Tuesday, January 28, 2025 at 05:42:14 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 22

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

\[ y(x)\to c_3 e^x+c_1 \cos (x)+c_2 \sin (x) \]