32.5.4 problem Exercise 11.4, page 97

Internal problem ID [5842]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.4, page 97
Date solved : Tuesday, March 04, 2025 at 11:47:56 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.066 (sec). Leaf size: 17

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

\[ x(y)\to e^{-y^2} (y+c_1) \]

✓ Sympy. Time used: 0.217 (sec). Leaf size: 10

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

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