20.4.41 problem Problem 59

Internal problem ID [3676]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 59
Date solved : Monday, January 27, 2025 at 07:54:29 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Riccati]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.120 (sec). Leaf size: 20

dsolve([diff(y(x),x)=2*x*(x+y(x))^2-1,y(0) = 1],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-x^{3}+x -1}{x^{2}-1} \]

✓ Solution by Mathematica

Time used: 0.155 (sec). Leaf size: 21

DSolve[{D[y[x],x]==2*x*(x+y[x])^2-1,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-x^3+x-1}{x^2-1} \]