10.6.13 problem 13

Internal problem ID [1230]
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
Date solved : Monday, January 27, 2025 at 04:46:06 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 11

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

\[ y = \tan \left (x^{2}+c_1 +x \right ) \]

✓ Solution by Mathematica

Time used: 0.187 (sec). Leaf size: 13

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

\[ y(x)\to \tan \left (x^2+x+c_1\right ) \]