15.9.24 problem 38

Internal problem ID [3081]
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 : 38
Date solved : Monday, January 27, 2025 at 07:19:14 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+24 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve(diff(y(x),x$3)-5*diff(y(x),x$2)-2*diff(y(x),x)+24*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_3 \,{\mathrm e}^{6 x}+{\mathrm e}^{5 x} c_{1} +c_2 \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 29

DSolve[D[y[x],{x,3}]-5*D[y[x],{x,2}]-2*D[y[x],x]+24*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (e^{5 x} \left (c_3 e^x+c_2\right )+c_1\right ) \]