12.1.3 problem Problem 14.2 (c)

Internal problem ID [3459]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number : Problem 14.2 (c)
Date solved : Tuesday, September 30, 2025 at 06:39:00 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

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

\[ y = \frac {x}{4+\ln \left (x \right ) x +c_1 x} \]

✓ Mathematica. Time used: 0.104 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \frac {2}{x^2-8 x-2 c_1}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \frac {x}{C_{1} x + x \log {\left (x \right )} + 4} \]