23.5.87 problem 87

Internal problem ID [6696]
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 : 87
Date solved : Friday, October 03, 2025 at 02:09:45 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} 10 y^{\prime }+8 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.036 (sec). Leaf size: 80

ode:=10*diff(y(x),x)+8*x*diff(y(x),x)+(x^2+1)*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 \int \left (x +i\right ) \operatorname {HeunC}\left (0, 1, -1, 16 i, \frac {21}{2}-8 i, -\frac {i x}{2}+\frac {1}{2}\right )d x +c_3 \int \left (x +i\right ) \operatorname {HeunC}\left (0, 1, -1, 16 i, \frac {21}{2}-8 i, -\frac {i x}{2}+\frac {1}{2}\right ) \int \frac {1}{\left (x +i\right )^{2} \operatorname {HeunC}\left (0, 1, -1, 16 i, \frac {21}{2}-8 i, -\frac {i x}{2}+\frac {1}{2}\right )^{2}}d x d x \]

✗ Mathematica

ode=10*D[y[x],x] + 8*x*D[y[x],x] + (1 + x^2)*D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*x*Derivative(y(x), x) + (x**2 + 1)*Derivative(y(x), (x, 3)) + 10*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**2 - 1)*Derivative(y(x), (x, 3))/(2*(4