40.4.16 problem 19 (r)

Internal problem ID [6656]
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)
Date solved : Monday, January 27, 2025 at 02:17:32 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} 1+y^{2}&=\left (\arctan \left (y\right )-x \right ) y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 18

dsolve((1+y(x)^2)=(arctan(y(x))-x)*diff(y(x),x),y(x), singsol=all)
 

\[ y = \tan \left (\operatorname {LambertW}\left (-c_1 \,{\mathrm e}^{-x -1}\right )+x +1\right ) \]

✓ Solution by Mathematica

Time used: 60.178 (sec). Leaf size: 21

DSolve[(1+y[x]^2)==(ArcTan[y[x]]-x)*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \tan \left (W\left (c_1 \left (-e^{-x-1}\right )\right )+x+1\right ) \]