23.3.572 problem 580

Internal problem ID [6286]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 580
Date solved : Tuesday, September 30, 2025 at 02:44:56 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y+\left (b x +a \right )^{4} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 39

ode:=y(x)+(b*x+a)^4*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (b x +a \right ) \left (c_1 \sin \left (\frac {1}{b \left (b x +a \right )}\right )+c_2 \cos \left (\frac {1}{b \left (b x +a \right )}\right )\right ) \]

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 57

ode=y[x] + (a + b*x)^4*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} e^{-\frac {i}{b (a+b x)}} (a+b x) \left (2 c_1 e^{\frac {2 i}{b (a+b x)}}-i c_2\right ) \end{align*}

✗ Sympy

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

False