84.2.5 problem 1.11

Internal problem ID [22074]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 1. Basic concepts. Supplementary problems
Problem number : 1.11
Date solved : Thursday, October 02, 2025 at 08:23:26 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} {r^{\prime \prime }}^{2}+r^{\prime \prime }+y r^{\prime }&=0 \end{align*}

✗ Maple

ode:=diff(diff(r(y),y),y)^2+diff(diff(r(y),y),y)+y*diff(r(y),y) = 0; 
dsolve(ode,r(y), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[r[y],{y,2}]^2+D[r[y],{y,2}]+y*D[r[y],y]==0; 
ic={}; 
DSolve[{ode,ic},r[y],y,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

NotImplementedError : The given ODE Derivative(r(y), y) - (-Derivative(r(y), (y, 2)) - 1)*Derivative(r(y), (y, 2))/y cannot be solved by the factorable group method