23.5.120 problem 120

Internal problem ID [6729]
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 : 120
Date solved : Tuesday, September 30, 2025 at 03:51:12 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 67

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

\[ y = \frac {\left (180 x^{5}+600 x^{3}+900 x \right ) \ln \left (x \right )-36 x^{5}+900 c_3 \,x^{4}+\left (-900 c_1 +100\right ) x^{3}+1800 c_3 \,x^{2}-2700 c_1 x -225 c_2 +900 c_3}{900 \left (x^{2}+1\right )^{2}} \]

✓ Mathematica. Time used: 0.355 (sec). Leaf size: 258

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

\begin{align*} 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 \end{align*}

✗ Sympy

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