15.10.18 problem 18

Internal problem ID [3105]
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 : 18
Date solved : Monday, January 27, 2025 at 07:19:30 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 43

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

\[ y = \left (c_2 \,{\mathrm e}^{4 x}+c_3 \sin \left (\frac {\sqrt {3}\, x}{2}\right ) {\mathrm e}^{\frac {3 x}{2}}+c_4 \cos \left (\frac {\sqrt {3}\, x}{2}\right ) {\mathrm e}^{\frac {3 x}{2}}+c_{1} \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 64

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

\[ y(x)\to e^{-2 x} \left (c_4 e^{4 x}+c_2 e^{3 x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 e^{3 x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+c_3\right ) \]