7.5.38 problem 38

Internal problem ID [142]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 38
Date solved : Friday, February 07, 2025 at 07:57:24 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: 0.063 (sec). Leaf size: 22

dsolve(( x+arctan(y(x)) )+( (x+y(x))/(1+y(x)^2) )*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.149 (sec). Leaf size: 30

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

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