Internal problem ID [116]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 38.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {x +\arctan \relax (y)+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.025 (sec). Leaf size: 22
dsolve(x+arctan(y(x))+(x+y(x))*diff(y(x),x)/(1+y(x)^2) = 0,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\RootOf \left (2 x \textit {\_Z} +x^{2}-2 \ln \left (\cos \left (\textit {\_Z} \right )\right )+2 c_{1}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.146 (sec). Leaf size: 30
DSolve[x+ArcTan[y[x]]+(x+y[x])*y'[x]/(1+y[x]^2) == 0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x \text {ArcTan}(y(x))+\frac {x^2}{2}+\frac {1}{2} \log \left (y(x)^2+1\right )=c_1,y(x)\right ] \]