7.10.44 problem 51

Internal problem ID [314]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 51
Date solved : Saturday, March 29, 2025 at 04:50:32 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} a \,x^{3} y^{\prime \prime \prime }+b \,x^{2} y^{\prime \prime }+c x y^{\prime }+d y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 1282

ode:=a*x^3*diff(diff(diff(y(x),x),x),x)+b*x^2*diff(diff(y(x),x),x)+c*x*diff(y(x),x)+d*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 144

ode=a*x^3*D[y[x],{x,3}]+b*x^2*D[y[x],{x,2}]+c*x*D[y[x],x]+d*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 x^{\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \left (\frac {b}{a}-3\right )+\text {$\#$1} \left (-\frac {b}{a}+\frac {c}{a}+2\right )+\frac {d}{a}\&,1\right ]}+c_2 x^{\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \left (\frac {b}{a}-3\right )+\text {$\#$1} \left (-\frac {b}{a}+\frac {c}{a}+2\right )+\frac {d}{a}\&,2\right ]}+c_3 x^{\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \left (\frac {b}{a}-3\right )+\text {$\#$1} \left (-\frac {b}{a}+\frac {c}{a}+2\right )+\frac {d}{a}\&,3\right ]} \]

✗ Sympy

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

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