49.3.1 problem 1(a)

Internal problem ID [7601]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1. Introduction– Linear equations of First Order. Page 45
Problem number : 1(a)
Date solved : Wednesday, March 05, 2025 at 04:47:35 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

ode:=diff(y(x),x)+2*x*y(x) = 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]+2*x*y[x]==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: 0.342 (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)
 

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