Internal problem ID [2196]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-2 x \left (x +y\right )^{2}+1=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.209 (sec). Leaf size: 20
dsolve([diff(y(x),x)=2*x*(x+y(x))^2-1,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {-x^{3}+x -1}{x^{2}-1} \]
✓ Solution by Mathematica
Time used: 0.143 (sec). Leaf size: 21
DSolve[{y'[x]==2*x*(x+y[x])^2-1,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-x^3+x-1}{x^2-1} \\ \end{align*}