56.38.11 problem Ex 11

Internal problem ID [14303]
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 62. Summary. Page 144
Problem number : Ex 11
Date solved : Thursday, October 02, 2025 at 09:30:25 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime }+8 x y^{\prime \prime }+4 x^{2} y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

ode:=4*x^2*diff(diff(diff(y(x),x),x),x)+8*x*diff(diff(y(x),x),x)+diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\ln \left (x \right ) c_3 +c_2 \right ) \sqrt {x}+c_1 \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 28

ode=4*x^2*D[y[x],{x,3}]+8*x*D[y[x],{x,2}]+D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sqrt {x} (c_2 \log (x)+2 c_1-2 c_2)+c_3 \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**2*Derivative(y(x), (x, 3)) + 8*x*Derivative(y(x), (x, 2)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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