15.10.21 problem 21

Internal problem ID [3108]
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 : 21
Date solved : Monday, January 27, 2025 at 07:19:31 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-12 y^{\prime }+16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 41

dsolve(diff(y(x),x$4)-3*diff(y(x),x$3)+4*diff(y(x),x$2)-12*diff(y(x),x)+16*y(x)=0,y(x), singsol=all)
 

\[ y = c_4 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {15}\, x}{2}\right )+c_3 \,{\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {15}\, x}{2}\right )+{\mathrm e}^{2 x} \left (c_2 x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 57

DSolve[D[y[x],{x,4}]-3*D[y[x],{x,3}]+4*D[y[x],{x,2}]-12*D[y[x],x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x/2} \left (e^{5 x/2} (c_4 x+c_3)+c_2 \cos \left (\frac {\sqrt {15} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {15} x}{2}\right )\right ) \]