64.10.43 problem 45

Internal problem ID [13449]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 45
Date solved : Tuesday, January 28, 2025 at 05:42:52 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+6 y^{\prime \prime }+2 y^{\prime }+5 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)+6*diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 40

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

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