83.11.1 problem 1

Internal problem ID [19168]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (C) at page 33
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:10:50 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

dsolve(diff(y(x),x$4)+8*diff(y(x),x$2)+16*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \left (c_4 x +c_{2} \right ) \cos \left (2 x \right )+\sin \left (2 x \right ) \left (c_3 x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

DSolve[D[y[x],{x,4}]+8*D[y[x],{x,2}]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (c_2 x+c_1) \cos (2 x)+(c_4 x+c_3) \sin (2 x) \]