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 = 0.051036 (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 = 0.06 (sec), leaf count = 52

\[ \left \{ y \relax (x ) ={\frac {\cos \left (2\,x \right ) {\it a1}\,{\it a2}+2\,\sin \left (2\,x \right ) {\it a1}\,{\it a2}\,x-2\,{x}^{2} \left ({\it a1}+2\,{\it a3} \right ) {\it a2}+8\,{\it \_C1}}{-4\,{\it a1}\,\cos \left (2\,x \right ) +8\,{\it a0}+4\,{\it a1}}} \right \} \] 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),'implicit')

Maple raw output

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