74.5.20 problem 20

Internal problem ID [15984]
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 : Tuesday, January 28, 2025 at 08:25:39 AM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 20

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

\[ x +y^{2}+2 y+2-{\mathrm e}^{y} c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.159 (sec). Leaf size: 37

DSolve[D[y[x],x]==1/(y[x]^2+x),y[x],x,IncludeSingularSolutions -> True]
 

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