60.4.53 problem 1511

Internal problem ID [11476]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1511
Date solved : Sunday, March 30, 2025 at 08:23:00 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-6 x^{3} \left (x -1\right ) \ln \left (x \right )+x^{3} \left (x +8\right )&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 49

ode:=x^3*diff(diff(diff(y(x),x),x),x)+3*x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+2*y(x)-6*x^3*(x-1)*ln(x)+x^3*(x+8) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (50 x^{6}-135 x^{5}+450 c_3 \,x^{3}\right ) \ln \left (x \right )-50 x^{6}-18 x^{5}+450 c_1 \,x^{3}+450 c_2}{450 x^{2}} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 52

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

\[ y(x)\to -\frac {x^4}{9}-\frac {x^3}{25}+\frac {c_1}{x^2}+\left (\frac {x^4}{9}-\frac {3 x^3}{10}+c_3 x\right ) \log (x)+c_2 x \]

✓ Sympy. Time used: 0.464 (sec). Leaf size: 46

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x**3*(x - 1)*log(x) + x**3*(x + 8) + x**3*Derivative(y(x), (x, 3)) + 3*x**2*Derivative(y(x), (x, 2)) - 2*x*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{2}} + C_{2} x + C_{3} x \log {\left (x \right )} + \frac {x^{4} \log {\left (x \right )}}{9} - \frac {x^{4}}{9} - \frac {3 x^{3} \log {\left (x \right )}}{10} - \frac {x^{3}}{25} \]