15.10.15 problem 15

Internal problem ID [3102]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 18, page 82
Problem number : 15
Date solved : Monday, January 27, 2025 at 07:19:28 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 37

dsolve(diff(y(x),x$4)+5*diff(y(x),x$2)+6*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \sin \left (\sqrt {2}\, x \right )+c_2 \cos \left (\sqrt {2}\, x \right )+c_3 \sin \left (\sqrt {3}\, x \right )+c_4 \cos \left (\sqrt {3}\, x \right ) \]

✓ Solution by Mathematica

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

DSolve[D[y[x],{x,4}]+5*D[y[x],{x,2}]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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