71.10.9 problem 9

Internal problem ID [14504]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 06:42:43 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35 y^{\prime \prime }+16 y^{\prime }-52 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 40

dsolve(diff(y(x),x$5)-diff(y(x),x$4)+diff(y(x),x$3)+35*diff(y(x),x$2)+16*diff(y(x),x)-52*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_4 \,{\mathrm e}^{4 x} \sin \left (3 x \right )+c_5 \,{\mathrm e}^{4 x} \cos \left (3 x \right )+{\mathrm e}^{3 x} c_{1} +c_{3} x +c_{2} \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 50

DSolve[D[y[x],{x,5}]-D[y[x],{x,4}]+D[y[x],{x,3}]+35*D[y[x],{x,2}]+16*D[y[x],x]-52*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (c_4 x+c_5 e^{3 x}+c_2 e^{4 x} \cos (3 x)+c_1 e^{4 x} \sin (3 x)+c_3\right ) \]