89.5.9 problem 9

Internal problem ID [24359]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 9
Date solved : Thursday, October 02, 2025 at 10:22:04 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ y = \frac {1}{2}+{\mathrm e}^{-x^{2}} c_1 \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 26

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

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

✓ Sympy. Time used: 0.191 (sec). Leaf size: 12

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

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