7.10.20 problem 20

Internal problem ID [290]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 20
Date solved : Wednesday, February 05, 2025 at 03:06:44 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 36

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

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 52

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

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