4.5.14 \(x y'(x)=y(x)-x \tan \left (\frac {y(x)}{x}\right )\)

ODE
\[ x y'(x)=y(x)-x \tan \left (\frac {y(x)}{x}\right ) \] ODE Classification

[[_homogeneous, `class A`], _dAlembert]

Book solution method
Homogeneous equation

Mathematica
cpu = 0.0314434 (sec), leaf count = 16

\[\left \{\left \{y(x)\to x \sin ^{-1}\left (\frac {e^{c_1}}{x}\right )\right \}\right \}\]

Maple
cpu = 0.012 (sec), leaf count = 17

\[ \left \{ -{\it \_C1}+\ln \left (\sin \left ({\frac {y \relax (x ) }{x}} \right ) \right ) +\ln \relax (x ) =0 \right \} \] Mathematica raw input

DSolve[x*y'[x] == -(x*Tan[y[x]/x]) + y[x],y[x],x]

Mathematica raw output

{{y[x] -> x*ArcSin[E^C[1]/x]}}

Maple raw input

dsolve(x*diff(y(x),x) = y(x)-x*tan(y(x)/x), y(x),'implicit')

Maple raw output

-_C1+ln(sin(y(x)/x))+ln(x) = 0