15.9.17 problem 31

Internal problem ID [3074]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 31
Date solved : Monday, January 27, 2025 at 07:19:11 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }-17 y^{\prime }+60 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)-17*diff(y(x),x)+60*y(x)=0,y(x), singsol=all)
 

\[ y = \left ({\mathrm e}^{9 x} c_{1} +c_2 \,{\mathrm e}^{7 x}+c_3 \right ) {\mathrm e}^{-4 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 30

DSolve[D[y[x],{x,3}]-4*D[y[x],{x,2}]-17*D[y[x],x]+60*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-4 x} \left (c_2 e^{7 x}+c_3 e^{9 x}+c_1\right ) \]