Internal problem ID [415]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Chapter 11 Power series methods. Section 11.1 Introduction and Review of power series. Page
615
Problem number: problem 26(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-1-y^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 6
dsolve([diff(y(x),x)=1+y(x)^2,y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \tan \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 7
DSolve[{y'[x]==1+y[x]^2,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan (x) \\ \end{align*}