9.2.18 problem problem 30

Internal problem ID [952]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with Constant Coefficients. Page 300
Problem number : problem 30
Date solved : Wednesday, February 05, 2025 at 04:51:18 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

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

\[ y = c_1 \,{\mathrm e}^{2 x}+c_2 \,{\mathrm e}^{-x}+c_3 \sin \left (\sqrt {3}\, x \right )+c_4 \cos \left (\sqrt {3}\, x \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 44

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

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