54.3.378 problem 1395

Internal problem ID [12673]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1395
Date solved : Wednesday, October 01, 2025 at 02:19:26 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 39

ode:=diff(diff(y(x),x),x) = -1/(a*x+b)^4*y(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.189 (sec). Leaf size: 62

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

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

✗ Sympy

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

False