15.10.23 problem 23

Internal problem ID [3110]
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 : 23
Date solved : Monday, January 27, 2025 at 07:19:32 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }-6 y^{\prime \prime }+8 y^{\prime }-8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 37

dsolve(diff(y(x),x$5)-diff(y(x),x$4)+6*diff(y(x),x$3)-6*diff(y(x),x$2)+8*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 48

DSolve[D[y[x],{x,5}]-D[y[x],{x,4}]+6*D[y[x],{x,3}]-6*D[y[x],{x,2}]+8*D[y[x],x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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