8.5.38 problem 38

Internal problem ID [766]
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
Date solved : Monday, January 27, 2025 at 03:04:16 AM
CAS classification : [_exact]

\begin{align*} x +\arctan \left (y\right )+\frac {\left (x +y\right ) y^{\prime }}{1+y^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.031 (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)
 

\[ y = \tan \left (\operatorname {RootOf}\left (2 x \textit {\_Z} +x^{2}-2 \ln \left (\cos \left (\textit {\_Z} \right )\right )+2 c_1 \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.146 (sec). Leaf size: 30

DSolve[x+ArcTan[y[x]]+(x+y[x])*D[y[x],x]/(1+y[x]^2) == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x \arctan (y(x))+\frac {x^2}{2}+\frac {1}{2} \log \left (y(x)^2+1\right )=c_1,y(x)\right ] \]