Internal problem ID [504]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-2 \left (x +1\right ) \left (1+y^{2}\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 10
dsolve([diff(y(x),x) = 2*(1+x)*(1+y(x)^2),y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \tan \left (x \left (2+x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.25 (sec). Leaf size: 11
DSolve[{y'[x] == 2*(1+x)*(1+y[x]^2),y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan (x (x+2)) \\ \end{align*}