##### 4.9.17 $$y'(x) \left (\text {a0}+\text {a1} \sin ^2(x)\right )+\text {a2} x \left (\text {a1} \sin ^2(x)+\text {a3}\right )+\text {a1} y(x) \sin (2 x)=0$$

ODE
$y'(x) \left (\text {a0}+\text {a1} \sin ^2(x)\right )+\text {a2} x \left (\text {a1} \sin ^2(x)+\text {a3}\right )+\text {a1} y(x) \sin (2 x)=0$ ODE Classiﬁcation

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.298948 (sec), leaf count = 58

$\left \{\left \{y(x)\to \frac {-2 \text {a1} \text {a2} x^2+2 \text {a1} \text {a2} x \sin (2 x)+\text {a1} \text {a2} \cos (2 x)-4 \text {a2} \text {a3} x^2+4 c_1}{4 (2 \text {a0}-\text {a1} \cos (2 x)+\text {a1})}\right \}\right \}$

Maple
cpu = 0.1 (sec), leaf count = 56

$\left [y \left (x \right ) = \frac {-2 \mathit {a2} x \mathit {a1} \sin \left (2 x \right )+2 \mathit {a2} \mathit {a1} \,x^{2}+4 \mathit {a2} \mathit {a3} \,x^{2}-\mathit {a2} \mathit {a1} \cos \left (2 x \right )-8 \textit {\_C1}}{4 \mathit {a1} \cos \left (2 x \right )-8 \mathit {a0} -4 \mathit {a1}}\right ]$ Mathematica raw input

DSolve[a2*x*(a3 + a1*Sin[x]^2) + a1*Sin[2*x]*y[x] + (a0 + a1*Sin[x]^2)*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (-2*a1*a2*x^2 - 4*a2*a3*x^2 + 4*C[1] + a1*a2*Cos[2*x] + 2*a1*a2*x*Sin[
2*x])/(4*(2*a0 + a1 - a1*Cos[2*x]))}}

Maple raw input

dsolve((a0+a1*sin(x)^2)*diff(y(x),x)+a2*x*(a3+a1*sin(x)^2)+a1*y(x)*sin(2*x) = 0, y(x))

Maple raw output

[y(x) = (-2*a2*x*a1*sin(2*x)+2*a2*a1*x^2+4*a2*a3*x^2-a2*a1*cos(2*x)-8*_C1)/(4*a1
*cos(2*x)-8*a0-4*a1)]