38.6.49 problem 49

Internal problem ID [8479]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 49
Date solved : Tuesday, September 30, 2025 at 05:37:55 PM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

\begin{align*} 1&=\left (x +y^{2}\right ) y^{\prime } \end{align*}

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

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

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

✓ Mathematica. Time used: 0.101 (sec). Leaf size: 37

ode=1==(x+y[x]^2)*D[y[x],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: 0.572 (sec). Leaf size: 27

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

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