60.4.47 problem 1503

Internal problem ID [11470]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1503
Date solved : Sunday, March 30, 2025 at 08:22:52 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime \prime }+8 x y^{\prime \prime }+10 y^{\prime }-3+\frac {1}{x^{2}}-2 \ln \left (x \right )&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 67

ode:=(x^2+1)*diff(diff(diff(y(x),x),x),x)+8*x*diff(diff(y(x),x),x)+10*diff(y(x),x)-3+1/x^2-2*ln(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (45 x^{5}+150 x^{3}+225 x \right ) \ln \left (x \right )-9 x^{5}+225 c_1 \,x^{4}+\left (225 c_2 -50\right ) x^{3}+450 c_1 \,x^{2}+\left (675 c_2 -225\right ) x +225 c_3}{225 \left (x^{2}+1\right )^{2}} \]

✓ Mathematica. Time used: 0.568 (sec). Leaf size: 258

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

\[ y(x)\to \frac {1}{225} \left (-3 (17+75 c_2) \arctan (x)-\frac {51 x}{x^2+1}-\frac {34 x}{\left (x^2+1\right )^2}-\frac {225 c_2 x}{x^2+1}-\frac {150 c_2 x}{\left (x^2+1\right )^2}-\frac {225 c_1}{4 \left (x^2+1\right )^2}-9 x+\frac {47}{x-i}+\frac {47}{x+i}+45 x \log (x)+60 i \log (-x+i)+\frac {171}{2} i \log (1-i x)-\frac {171}{2} i \log (1+i x)+\frac {30 \log (x)}{x-i}+\frac {30 \log (x)}{x+i}-\frac {30 i \log (x)}{(x-i)^2}+\frac {30 i \log (x)}{(x+i)^2}-60 i \log (x+i)+\frac {75 c_2}{x-i}+\frac {75 c_2}{x+i}+\frac {225}{2} i c_2 \log (1-i x)-\frac {225}{2} i c_2 \log (1+i x)\right )+c_3 \]

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (x**2*(-x**2*Derivative(y(x), (x, 3)) - 8*x*Derivative(y(x), (x, 2)) + 2*log(x) - Derivative(y(x), (x, 3)) + 3) - 1)/(10*x**2) cannot be solved by the factorable group method