68.5.20 problem 20

Internal problem ID [17271]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 20
Date solved : Thursday, October 02, 2025 at 02:00:33 PM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

\begin{align*} y^{\prime }&=\frac {1}{x +y^{2}} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 20

ode:=diff(y(x),x) = 1/(x+y(x)^2); 
dsolve(ode,y(x), singsol=all);
 

\[ x +y^{2}+2 y+2-{\mathrm e}^{y} c_1 = 0 \]

✓ Mathematica. Time used: 0.11 (sec). Leaf size: 37

ode=D[y[x],x]==1/(y[x]^2+x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x=e^{y(x)} \int _1^{y(x)}e^{-K[1]} K[1]^2dK[1]+c_1 e^{y(x)},y(x)\right ] \]

✓ Sympy. Time used: 0.449 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1/(x + y(x)**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} + x e^{- y{\left (x \right )}} - \left (- y^{2}{\left (x \right )} - 2 y{\left (x \right )} - 2\right ) e^{- y{\left (x \right )}} = 0 \]