83.33.1 problem 1

Internal problem ID [19409]
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 : 1
Date solved : Tuesday, January 28, 2025 at 01:38:46 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 38

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

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