11.2.11 problem 18

Internal problem ID [1482]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 4.2, Higher order linear differential equations. Constant coefficients. page 180
Problem number : 18
Date solved : Monday, January 27, 2025 at 04:57:49 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+6 y^{\prime \prime }+30 y^{\prime }-36 y&=0 \end{align*}

Solution by Maple

Time used: 0.003 (sec). Leaf size: 38

dsolve(diff(y(x),x$4)-7*diff(y(x),x$3)+6*diff(y(x),x$2)+30*diff(y(x),x)-36*y(x)=0,y(x), singsol=all)
 
\[ y = \left ({\mathrm e}^{5 x} c_2 +c_3 \,{\mathrm e}^{x \left (5+\sqrt {3}\right )}+c_4 \,{\mathrm e}^{-x \left (-5+\sqrt {3}\right )}+c_1 \right ) {\mathrm e}^{-2 x} \]

Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 51

DSolve[D[y[x],{x,4}]-7*D[y[x],{x,3}]+6*D[y[x],{x,2}]+30*D[y[x],x]-36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to c_1 e^{-\left (\left (\sqrt {3}-3\right ) x\right )}+c_2 e^{\left (3+\sqrt {3}\right ) x}+c_3 e^{-2 x}+c_4 e^{3 x} \]