23.5.82 problem 82

Internal problem ID [6691]
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 : 82
Date solved : Tuesday, September 30, 2025 at 03:50:52 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} 4 y^{\prime }+5 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime }&=\ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 32

ode:=4*diff(y(x),x)+5*x*diff(diff(y(x),x),x)+x^2*diff(diff(diff(y(x),x),x),x) = ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (x^{2}+4 c_2 \right ) \ln \left (x \right )-2 x^{2}+4 c_1 x +4 c_3}{4 x} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 43

ode=4*D[y[x],x] + 5*x*D[y[x],{x,2}] + x^2*D[y[x],{x,3}] == Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\left (x^2-8 c_2\right ) \log (x)-2 \left (x^2-2 c_3 x+2 c_1+4 c_2\right )}{4 x} \end{align*}

✓ Sympy. Time used: 0.181 (sec). Leaf size: 24

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

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