Internal problem ID [3016]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan,
1960
Section: Exercises, page 14
Problem number: 2(e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {{\mathrm e}^{-y}+\left (x^{2}+1\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 11
dsolve([exp(-y(x))+(1+x^2)*diff(y(x),x)=0,y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (-\arctan \left (x \right )+1\right ) \]
✓ Solution by Mathematica
Time used: 0.391 (sec). Leaf size: 12
DSolve[{Exp[-y[x]]+(1+x^2)*y'[x]==0,y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \log (1-\arctan (x)) \]