15.9.27 problem 41

Internal problem ID [3084]
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 : 41
Date solved : Monday, January 27, 2025 at 07:19:15 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-13 y^{\prime \prime \prime }-13 y^{\prime \prime }+36 y^{\prime }+36 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 33

dsolve(diff(y(x),x$5)+diff(y(x),x$4)-13*diff(y(x),x$3)-13*diff(y(x),x$2)+36*diff(y(x),x)+36*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_{1} {\mathrm e}^{6 x}+c_4 \,{\mathrm e}^{5 x}+c_5 \,{\mathrm e}^{2 x}+c_2 \,{\mathrm e}^{x}+c_3 \right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 42

DSolve[D[y[x],{x,5}]+D[y[x],{x,4}]-13*D[y[x],{x,3}]-13*D[y[x],{x,2}]+36*D[y[x],x]+36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (e^x \left (c_3 e^x+e^{4 x} \left (c_5 e^x+c_4\right )+c_2\right )+c_1\right ) \]