15.32 problem 440

Internal problem ID [3186]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 15
Problem number: 440.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x)*G(y),0]]]

Solve \begin {gather*} \boxed {\left (x +y\right ) y^{\prime }+\tan \relax (y)=0} \end {gather*}

Solution by Maple

Time used: 0.195 (sec). Leaf size: 26

dsolve((x+y(x))*diff(y(x),x)+tan(y(x)) = 0,y(x), singsol=all)
 

\[ x -\frac {-\cos \left (y \relax (x )\right )-y \relax (x ) \sin \left (y \relax (x )\right )+c_{1}}{\sin \left (y \relax (x )\right )} = 0 \]

Solution by Mathematica

Time used: 0.21 (sec). Leaf size: 29

DSolve[(x+y[x])y'[x]+Tan[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}[x=\csc (y(x)) (-y(x) \sin (y(x))-\cos (y(x)))+c_1 \csc (y(x)),y(x)] \]