Internal problem ID [11664]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 8, Separable equations. Exercises page 72
Problem number: 8.1 (ii).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\left (y^{2}+1\right ) \tan \left (x \right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 12
dsolve([diff(y(x),x)=(1+y(x)^2)*tan(x),y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \cot \left (\frac {\pi }{4}+\ln \left (\cos \left (x \right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.472 (sec). Leaf size: 15
DSolve[{y'[x]==(1+y[x]^2)*Tan[x],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \cot \left (\log (\cos (x))+\frac {\pi }{4}\right ) \]