40.8.8 problem 23

Internal problem ID [6708]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 13. Homogeneous Linear equations with constant coefficients. Supplemetary problems. Page 86
Problem number : 23
Date solved : Monday, January 27, 2025 at 02:24:34 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

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

\[ y = c_1 +c_2 x +c_3 \sin \left (2 x \right )+c_4 \cos \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 32

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

\[ y(x)\to c_4 x-\frac {1}{4} c_1 \cos (2 x)-\frac {1}{4} c_2 \sin (2 x)+c_3 \]