83.35.3 problem 3

Internal problem ID [19423]
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. Misc. Exercise on chapter VII. Page 118
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:39:30 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(a*diff(y(x),x$3)=diff(y(x),x$2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 25

DSolve[a*D[y[x],{x,3}]==D[y[x],{x,2}],y[x],x,IncludeSingularSolutions -> True]
 

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