15.10.16 problem 16

Internal problem ID [3103]
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 : 16
Date solved : Monday, January 27, 2025 at 07:19:29 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-8 y^{\prime }+8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 41

DSolve[D[y[x],{x,4}]-4*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]
 

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