Internal problem ID [5313]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary
problems. Page 39
Problem number: 19 (r).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]
\[ \boxed {y^{2}-\left (\arctan \left (y\right )-x \right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve((1+y(x)^2)=(arctan(y(x))-x)*diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{-x -1}\right )+x +1\right ) \]
✓ Solution by Mathematica
Time used: 60.157 (sec). Leaf size: 21
DSolve[(1+y[x]^2)==(ArcTan[y[x]]-x)*y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \tan \left (W\left (c_1 \left (-e^{-x-1}\right )\right )+x+1\right ) \]