67.2.4 problem 3.4 d

Internal problem ID [16314]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 3. Some basics about First order equations. Additional exercises. page 63
Problem number : 3.4 d
Date solved : Thursday, October 02, 2025 at 01:18:39 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 9

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

\[ y = \tanh \left (\ln \left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.299 (sec). Leaf size: 40

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

\begin{align*} y(x)&\to \frac {x^2-e^{2 c_1}}{x^2+e^{2 c_1}}\\ y(x)&\to -1\\ y(x)&\to 1 \end{align*}

✓ Sympy. Time used: 0.187 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \frac {C_{1} + x^{2}}{- C_{1} + x^{2}} \]