35.5.14 problem 25

Internal problem ID [6148]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page 414
Problem number : 25
Date solved : Monday, January 27, 2025 at 01:38:27 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

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

\[ y = \left (c_3 \,{\mathrm e}^{5 x}+c_1 \,{\mathrm e}^{3 x}+c_2 \right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 30

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

\[ y(x)\to -\frac {1}{3} c_1 e^{-3 x}+\frac {1}{2} c_2 e^{2 x}+c_3 \]