64.10.20 problem 20

Internal problem ID [13426]
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 : 20
Date solved : Tuesday, January 28, 2025 at 05:42:15 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

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

\[ y = \left (c_4 x +c_{3} \right ) {\mathrm e}^{-x}+{\mathrm e}^{2 x} c_{1} +{\mathrm e}^{x} c_{2} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 33

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

\[ y(x)\to e^{-x} \left (c_2 x+e^{2 x} \left (c_4 e^x+c_3\right )+c_1\right ) \]