23.5.180 problem 180

Internal problem ID [6789]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 180
Date solved : Tuesday, September 30, 2025 at 03:51:42 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} \operatorname {A4} y+\operatorname {A3} x y^{\prime }+\operatorname {A2} \,x^{2} y^{\prime \prime }+\operatorname {A1} \,x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 51

ode:=A4*y(x)+A3*x*diff(y(x),x)+A2*x^2*diff(diff(y(x),x),x)+A1*x^3*diff(diff(diff(y(x),x),x),x)+x^4*diff(diff(diff(diff(y(x),x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}x^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+\left (\operatorname {A1} -6\right ) \textit {\_Z}^{3}+\left (\operatorname {A2} -3 \operatorname {A1} +11\right ) \textit {\_Z}^{2}+\left (\operatorname {A3} -\operatorname {A2} +2 \operatorname {A1} -6\right ) \textit {\_Z} +\operatorname {A4} , \operatorname {index} =\textit {\_a} \right )} \textit {\_C}_{\textit {\_a}} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 186

ode=A4*y[x] + A3*x*D[y[x],x] + A2*x^2*D[y[x],{x,2}] + A1*x^3*D[y[x],{x,3}] + x^4*D[y[x],{x,4}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 x^{\text {Root}\left [\text {$\#$1}^4+\text {$\#$1}^3 (\text {A1}-6)+\text {$\#$1}^2 (-3 \text {A1}+\text {A2}+11)+\text {$\#$1} (2 \text {A1}-\text {A2}+\text {A3}-6)+\text {A4}\&,1\right ]}+c_2 x^{\text {Root}\left [\text {$\#$1}^4+\text {$\#$1}^3 (\text {A1}-6)+\text {$\#$1}^2 (-3 \text {A1}+\text {A2}+11)+\text {$\#$1} (2 \text {A1}-\text {A2}+\text {A3}-6)+\text {A4}\&,2\right ]}+c_3 x^{\text {Root}\left [\text {$\#$1}^4+\text {$\#$1}^3 (\text {A1}-6)+\text {$\#$1}^2 (-3 \text {A1}+\text {A2}+11)+\text {$\#$1} (2 \text {A1}-\text {A2}+\text {A3}-6)+\text {A4}\&,3\right ]}+c_4 x^{\text {Root}\left [\text {$\#$1}^4+\text {$\#$1}^3 (\text {A1}-6)+\text {$\#$1}^2 (-3 \text {A1}+\text {A2}+11)+\text {$\#$1} (2 \text {A1}-\text {A2}+\text {A3}-6)+\text {A4}\&,4\right ]} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
A1 = symbols("A1") 
A2 = symbols("A2") 
A3 = symbols("A3") 
A4 = symbols("A4") 
y = Function("y") 
ode = Eq(A1*x**3*Derivative(y(x), (x, 3)) + A2*x**2*Derivative(y(x), (x, 2)) + A3*x*Derivative(y(x), x) + A4*y(x) + x**4*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-A4*y(x) + x**2*(-A1*x*Derivative(y(x), (