15.9.30 problem 44

Internal problem ID [3087]
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 : 44
Date solved : Monday, January 27, 2025 at 07:19:17 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime }+2 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 30

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

\[ y = c_{1} +c_2 \sin \left (\sqrt {2}\, x \right )+c_3 \cos \left (\sqrt {2}\, x \right )+c_4 \sin \left (x \right )+c_5 \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.074 (sec). Leaf size: 52

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

\[ y(x)\to -c_4 \cos (x)-\frac {c_2 \cos \left (\sqrt {2} x\right )}{\sqrt {2}}+c_3 \sin (x)+\frac {c_1 \sin \left (\sqrt {2} x\right )}{\sqrt {2}}+c_5 \]