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]
\[ \boxed {\arctan \left (y\right )+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}}=-x} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \tan \left (\operatorname {RootOf}\left (2 x \textit {\_Z} +x^{2}-2 \ln \left (\cos \left (\textit {\_Z} \right )\right )+2 c_{1} \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.137 (sec). Leaf size: 30
DSolve[x+ArcTan[y[x]]+(x+y[x])*y'[x]/(1+y[x]^2) == 0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x \arctan (y(x))+\frac {x^2}{2}+\frac {1}{2} \log \left (y(x)^2+1\right )=c_1,y(x)\right ] \]