83.33.2 problem 2

Internal problem ID [19410]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (G) at page 115
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 01:38:47 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 34

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

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