83.11.4 problem 4

Internal problem ID [19171]
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 : 4
Date solved : Tuesday, January 28, 2025 at 01:10:51 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

dsolve(diff(y(x),x$4)-y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 30

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

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