ODE No. 1432

$$y^{″}(x)=-\cot (x)y^{\prime }(x)-\frac{1}{4}y(x)(-17{\sin }^2(x)-1){\csc }^2(x)$$ ✓ Mathematica : cpu = 0.0638446 (sec), leaf count = 37

DSolve[Derivative[2][y][x] == -1/4*(Csc[x]^2*(-1 - 17*Sin[x]^2)*y[x]) - Cot[x]*Derivative[1][y][x],y[x],x]
 

$$\left\{\{y(x)\to \frac{c_1{e}^{-2x}}{\sqrt{\sin (x)}}+\frac{c_2{e}^{2x}}{4\sqrt{\sin (x)}}\}\right\}$$ ✓ Maple : cpu = 0.042 (sec), leaf count = 22

dsolve(diff(diff(y(x),x),x) = -1/sin(x)*cos(x)*diff(y(x),x)-1/4*(-17*sin(x)^2-1)/sin(x)^2*y(x),y(x))
 

$$y\left(x\right)=\frac{c_2\cosh \left(2x\right)+c_1\sinh \left(2x\right)}{\sqrt{\sin \left(x\right)}}$$