Internal problem ID [580]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-1-2 x -y^{2}-2 x y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 11
dsolve(diff(y(x),x) = 1+2*x+y(x)^2+2*x*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (x^{2}+c_{1}+x \right ) \]
✓ Solution by Mathematica
Time used: 0.205 (sec). Leaf size: 13
DSolve[y'[x] == 1+2*x+y[x]^2+2*x*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan \left (x^2+x+c_1\right ) \\ \end{align*}