71.10.2 problem 2

Internal problem ID [14497]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 06:42:40 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+6 y^{\prime }-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x$3)-4*diff(y(x),x$2)+6*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 26

DSolve[D[y[x],{x,3}]-4*D[y[x],{x,2}]+6*D[y[x],x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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