83.33.1 problem 1

Internal problem ID [19338]
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 : Monday, March 31, 2025 at 07:08:59 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 26

ode:=a^2*diff(diff(diff(diff(y(x),x),x),x),x) = diff(diff(y(x),x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 x +c_3 \,{\mathrm e}^{\frac {x}{a}}+c_4 \,{\mathrm e}^{-\frac {x}{a}} \]

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 38

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

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

✓ Sympy. Time used: 0.083 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a**2*Derivative(y(x), (x, 4)) - Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} e^{- \frac {x}{a}} + C_{4} e^{\frac {x}{a}} \]