40.8.7 problem 22

Internal problem ID [6707]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 13. Homogeneous Linear equations with constant coefficients. Supplemetary problems. Page 86
Problem number : 22
Date solved : Monday, January 27, 2025 at 02:24:34 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+9 y^{\prime }-9 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(diff(y(x),x$3)-diff(y(x),x$2)+9*diff(y(x),x)-9*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 26

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]+9*D[y[x],x]-9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 e^x+c_1 \cos (3 x)+c_2 \sin (3 x) \]