62.36.6 problem Ex 6

Internal problem ID [12933]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 60. Exact equation. Integrating factor. Page 139
Problem number : Ex 6
Date solved : Monday, March 31, 2025 at 07:25:00 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

ode:=x^5*diff(diff(y(x),x),x)+(2*x^4-x)*diff(y(x),x)-(2*x^3-1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \left ({\mathrm e}^{-\frac {1}{3 x^{3}}} c_2 +c_1 \right ) \]

✓ Mathematica. Time used: 0.127 (sec). Leaf size: 31

ode=x^5*D[y[x],{x,2}]+(2*x^4-x)*D[y[x],x]-(2*x^3-1)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x \left (c_2 e^{\frac {22}{3}-\frac {1}{3 x^3}}+c_1\right )}{e^{11/6}} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**5*Derivative(y(x), (x, 2)) - (2*x**3 - 1)*y(x) + (2*x**4 - x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**5*Derivative(y(x), (x, 2)) + 2*x**3*y(x) - y(x))/(2*x**4 - x) cannot be solved by the factorable group method