83.35.3 problem 3

Internal problem ID [19344]
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 : Thursday, March 13, 2025 at 02:16:35 PM
CAS classification : [[_3rd_order, _missing_x]]

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

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

ode:=a*diff(diff(diff(y(x),x),x),x) = diff(diff(y(x),x),x); 
dsolve(ode,y(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.051 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a*Derivative(y(x), (x, 3)) - Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} e^{\frac {x}{a}} \]