23.5.61 problem 61

Internal problem ID [6670]
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 : 61
Date solved : Friday, October 03, 2025 at 02:09:38 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} -8 a x y-2 \left (-4 x^{2}-2 a +1\right ) y^{\prime }-6 x y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.089 (sec). Leaf size: 59

ode:=-8*a*x*y(x)-2*(-4*x^2-2*a+1)*diff(y(x),x)-6*x*diff(diff(y(x),x),x)+diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{2} \left (\operatorname {KummerU}\left (\frac {1}{2}-\frac {a}{4}, \frac {3}{2}, x^{2}\right )^{2} c_2 +\operatorname {KummerU}\left (\frac {1}{2}-\frac {a}{4}, \frac {3}{2}, x^{2}\right ) \operatorname {KummerM}\left (\frac {1}{2}-\frac {a}{4}, \frac {3}{2}, x^{2}\right ) c_3 +\operatorname {KummerM}\left (\frac {1}{2}-\frac {a}{4}, \frac {3}{2}, x^{2}\right )^{2} c_1 \right ) \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 57

ode=-8*a*x*y[x] - 2*(1 - 2*a - 4*x^2)*D[y[x],x] - 6*x*D[y[x],{x,2}] + D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 \operatorname {HermiteH}\left (\frac {a}{2},x\right ) \operatorname {Hypergeometric1F1}\left (-\frac {a}{4},\frac {1}{2},x^2\right )+c_1 \operatorname {HermiteH}\left (\frac {a}{2},x\right )^2+c_3 \operatorname {Hypergeometric1F1}\left (-\frac {a}{4},\frac {1}{2},x^2\right )^2 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-8*a*x*y(x) - 6*x*Derivative(y(x), (x, 2)) - (-4*a - 8*x**2 + 2)*Derivative(y(x), x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (8*a*x*y(x) + 6*x*Derivative(y(x), (x, 2))