15.10.9 problem 9

Internal problem ID [3096]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 18, page 82
Problem number : 9
Date solved : Monday, January 27, 2025 at 07:19:24 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+16 y^{\prime }-12 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(diff(y(x),x$3)-7*diff(y(x),x$2)+16*diff(y(x),x)-12*y(x)=0,y(x), singsol=all)
 

\[ y = \left (x c_3 +c_2 \right ) {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{3 x} \]

✓ Solution by Mathematica

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

DSolve[D[y[x],{x,3}]-7*D[y[x],{x,2}]+16*D[y[x],x]-12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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