23.5.122 problem 122

Internal problem ID [6731]
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 : 122
Date solved : Tuesday, September 30, 2025 at 03:51:13 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} 4 x^{2} y^{\prime }-4 x^{3} y^{\prime \prime }+4 x^{4} y^{\prime \prime \prime }&=1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 34

ode:=4*x^2*diff(y(x),x)-4*x^3*diff(diff(y(x),x),x)+4*x^4*diff(diff(diff(y(x),x),x),x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {18 x^{3} c_1 \ln \left (x \right )-1+\left (-9 c_1 +18 c_2 \right ) x^{3}+36 c_3 x}{36 x} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 42

ode=4*x^2*D[y[x],x] - 4*x^3*D[y[x],{x,2}] + 4*x^4*D[y[x],{x,3}] == 1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{4} (2 c_1-c_2) x^2+\frac {1}{2} c_2 x^2 \log (x)-\frac {1}{36 x}+c_3 \end{align*}

✓ Sympy. Time used: 0.191 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**4*Derivative(y(x), (x, 3)) - 4*x**3*Derivative(y(x), (x, 2)) + 4*x**2*Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x^{2} + C_{3} x^{2} \log {\left (x \right )} - \frac {1}{36 x} \]