64.10.13 problem 13

Internal problem ID [13419]
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 : 13
Date solved : Tuesday, January 28, 2025 at 05:42:13 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(diff(y(x),x$3)-5*diff(y(x),x$2)+7*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 24

DSolve[D[y[x],{x,3}]-5*D[y[x],{x,2}]+7*D[y[x],x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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