60.4.58 problem 1516

Internal problem ID [11481]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1516
Date solved : Sunday, March 30, 2025 at 08:23:05 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+\left (x +3\right ) x^{2} y^{\prime \prime }+5 \left (x -6\right ) x y^{\prime }+\left (4 x +30\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 188

ode:=x^3*diff(diff(diff(y(x),x),x),x)+(x+3)*x^2*diff(diff(y(x),x),x)+5*(x-6)*x*diff(y(x),x)+(4*x+30)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_3 \,{\mathrm e}^{-x} \left (x^{8}+28 x^{7}+450 x^{6}+5100 x^{5}+42900 x^{4}+267120 x^{3}+1179360 x^{2}+3326400 x +4536000\right ) \operatorname {Ei}_{1}\left (-x \right )+c_2 \,{\mathrm e}^{-x} \left (x^{8}+28 x^{7}+450 x^{6}+5100 x^{5}+42900 x^{4}+267120 x^{3}+1179360 x^{2}+3326400 x +4536000\right )+60 c_3 \left (x^{4}-84 x^{3}+2016 x^{2}-20160 x +75600\right ) \ln \left (x \right )+c_3 \,x^{7}+29 c_3 \,x^{6}+480 c_3 \,x^{5}+\left (c_1 +5612 c_3 \right ) x^{4}+\left (-84 c_1 +40152 c_3 \right ) x^{3}+\left (2016 c_1 +654192 c_3 \right ) x^{2}+\left (-20160 c_1 -2761920 c_3 \right ) x +75600 c_1 [phone] c_3}{x^{6}} \]

✗ Mathematica

ode=(30 + 4*x)*y[x] + 5*(-6 + x)*x*D[y[x],x] + x^2*(3 + x)*D[y[x],{x,2}] + x^3*Derivative[3][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + x**2*(x + 3)*Derivative(y(x), (x, 2)) + x*(5*x - 30)*Derivative(y(x), x) + (4*x + 30)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**3*Derivative(y(x), (x, 2)) - x**3*Derivative(y(x), (x, 3)) - 3*x**2*Derivative(y(x), (x, 2)) - 4*x*y(x) - 30*y(x))/(5*x*(x - 6)) cannot be solved by the factorable group method