ODE
\[ 2 y'(x)=2 \sin ^2(y(x)) \tan (y(x))-x \sin (2 y(x)) \] ODE Classification
[`y=_G(x,y')`]
Book solution method
Change of Variable, new dependent variable
Mathematica ✓
cpu = 0.361296 (sec), leaf count = 61
\[\left \{\left \{y(x)\to -\cot ^{-1}\left (\sqrt {e^{x^2} \left (4 c_1-\sqrt {\pi } \text {erf}(x)\right )}\right )\right \},\left \{y(x)\to \cot ^{-1}\left (\sqrt {e^{x^2} \left (4 c_1-\sqrt {\pi } \text {erf}(x)\right )}\right )\right \}\right \}\]
Maple ✗
cpu = 39.009 (sec), leaf count = 0 , could not solve
dsolve(2*diff(y(x),x) = 2*sin(y(x))^2*tan(y(x))-x*sin(2*y(x)), y(x),'implicit')
Mathematica raw input
DSolve[2*y'[x] == -(x*Sin[2*y[x]]) + 2*Sin[y[x]]^2*Tan[y[x]],y[x],x]
Mathematica raw output
{{y[x] -> -ArcCot[Sqrt[E^x^2*(4*C[1] - Sqrt[Pi]*Erf[x])]]}, {y[x] -> ArcCot[Sqrt[E^x^2*(4*C[1] - Sqrt[Pi]*Erf[x])]]}}
Maple raw input
dsolve(2*diff(y(x),x) = 2*sin(y(x))^2*tan(y(x))-x*sin(2*y(x)), y(x),'implicit')
Maple raw output
dsolve(2*diff(y(x),x) = 2*sin(y(x))^2*tan(y(x))-x*sin(2*y(x)), y(x),'implicit')