83.35.4 problem 4

Internal problem ID [19345]
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 : 4
Date solved : Thursday, March 13, 2025 at 02:16:36 PM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} x^{2} y^{\prime \prime \prime \prime }+1&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 32

ode:=x^2*diff(diff(diff(diff(y(x),x),x),x),x)+1 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {\ln \left (x \right ) x^{2}}{2}+\frac {c_{1} x^{3}}{6}+\frac {\left (2 c_{2} -3\right ) x^{2}}{4}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 37

ode=x^2*D[y[x],{x,4}]+1==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_4 x^3+\frac {1}{2} x^2 \log (x)+\left (-\frac {3}{4}+c_3\right ) x^2+c_2 x+c_1 \]

✓ Sympy. Time used: 0.243 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 4)) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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