Internal problem ID [3475]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 742.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (1+\left (x +y\right ) \tan \relax (y)\right ) y^{\prime }+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 13
dsolve((1+(x+y(x))*tan(y(x)))*diff(y(x),x)+1 = 0,y(x), singsol=all)
\[ x -\cos \left (y \relax (x )\right ) c_{1}+y \relax (x ) = 0 \]
✓ Solution by Mathematica
Time used: 0.182 (sec). Leaf size: 16
DSolve[(1+(x+y[x]) Tan[y[x]])y'[x]+1==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[x=-y(x)+c_1 \cos (y(x)),y(x)] \]