15.9.19 problem 33

Internal problem ID [3076]
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 : 33
Date solved : Monday, January 27, 2025 at 07:19:12 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-7 y^{\prime \prime }-y^{\prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

dsolve(diff(y(x),x$4)+diff(y(x),x$3)-7*diff(y(x),x$2)-diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_3 \,{\mathrm e}^{5 x}+c_2 \,{\mathrm e}^{4 x}+c_4 \,{\mathrm e}^{2 x}+c_{1} \right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 36

DSolve[D[y[x],{x,4}]+D[y[x],{x,3}]-7*D[y[x],{x,2}]-D[y[x],x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-3 x}+c_2 e^{-x}+c_3 e^x+c_4 e^{2 x} \]