Internal problem ID [3983]
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]]
\[ \boxed {\left (1+\tan \left (y\right ) \left (x +y\right )\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
dsolve((1+(x+y(x))*tan(y(x)))*diff(y(x),x)+1 = 0,y(x), singsol=all)
\[ x -c_{1} \cos \left (y \left (x \right )\right )+y \left (x \right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.473 (sec). Leaf size: 66
DSolve[(1+(x+y[x]) Tan[y[x]])y'[x]+1==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=\cos (y(x)) \left (-y(x) \sec (y(x))-\coth ^{-1}(\sin (y(x)))-\log \left (\cos \left (\frac {y(x)}{2}\right )-\sin \left (\frac {y(x)}{2}\right )\right )+\log \left (\sin \left (\frac {y(x)}{2}\right )+\cos \left (\frac {y(x)}{2}\right )\right )\right )+c_1 \cos (y(x)),y(x)\right ] \]