Internal problem ID [5943]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 1. Introduction– Linear equations of First Order. Page 45
Problem number: 14(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y^{2}=1} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 6
dsolve([diff(y(x),x)=1+y(x)^2,y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 7
DSolve[{y'[x]==1+y[x]^2,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \tan (x) \]