83.33.5 problem 5

Internal problem ID [19342]
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 : 5
Date solved : Monday, March 31, 2025 at 07:09:03 PM
CAS classification : [[_high_order, _missing_y]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 39

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

\[ y = c_1 +c_2 x +c_3 \,x^{\frac {5}{2}+\frac {\sqrt {1+4 \lambda }}{2}}+c_4 \,x^{\frac {5}{2}-\frac {\sqrt {1+4 \lambda }}{2}} \]

✓ Mathematica. Time used: 0.271 (sec). Leaf size: 98

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

\[ y(x)\to \frac {x^{\frac {5}{2}-\frac {1}{2} i \sqrt {-4 \lambda -1}} \left (c_1 \left (\lambda +2 i \sqrt {-4 \lambda -1}+4\right )+c_2 \left (\lambda -2 i \sqrt {-4 \lambda -1}+4\right ) x^{i \sqrt {-4 \lambda -1}}\right )}{(\lambda -6) (\lambda -2)}+c_4 x+c_3 \]

✗ Sympy

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

NotImplementedError : CRootOf is not supported over ZZ[lambda_]