84.18.5 problem 10.13

Internal problem ID [22202]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 10. Linear differential equations. General remarks. Supplementary problems
Problem number : 10.13
Date solved : Thursday, October 02, 2025 at 08:34:03 PM
CAS classification : [NONE]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (4*x*y(x)**2 - y(x) - Derivative(y(x), (x, 2)))/(2*x) cannot be solved by the factorable group method