##### 4.3.42 $$2 y'(x)=2 \sin ^2(y(x)) \tan (y(x))-x \sin (2 y(x))$$

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 = 0.676483 (sec), leaf count = 61

$\left \{\left \{y(x)\to -\cot ^{-1}\left (\sqrt {e^{x^2} \left (-\sqrt {\pi } \text {erf}(x)+4 c_1\right )}\right )\right \},\left \{y(x)\to \cot ^{-1}\left (\sqrt {e^{x^2} \left (-\sqrt {\pi } \text {erf}(x)+4 c_1\right )}\right )\right \}\right \}$

Maple
cpu = 75.304 (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))

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))

Maple raw output

dsolve(2*diff(y(x),x) = 2*sin(y(x))^2*tan(y(x))-x*sin(2*y(x)), y(x))