2.1418   ODE No. 1418

\[ y''(x)=\frac {y(x) \sin (x)}{x \cos (x)-\sin (x)}-\frac {x \sin (x) y'(x)}{x \cos (x)-\sin (x)} \]

✓ Mathematica : cpu = 0.113355 (sec), leaf count = 15

DSolve[Derivative[2][y][x] == (Sin[x]*y[x])/(x*Cos[x] - Sin[x]) - (x*Sin[x]*Derivative[1][y][x])/(x*Cos[x] - Sin[x]),y[x],x]
 

\[\{\{y(x)\to c_1 x+c_2 \sin (x)\}\}\]

✓ Maple : cpu = 6.048 (sec), leaf count = 44

dsolve(diff(diff(y(x),x),x) = -x*sin(x)/(cos(x)*x-sin(x))*diff(y(x),x)+sin(x)/(cos(x)*x-sin(x))*y(x),y(x))
 

\[y \left (x \right ) = \sin \left (x \right ) \left (\left (\int {\mathrm e}^{\int \frac {2 \cos \left (x \right ) \cot \left (x \right ) x -3 \cos \left (x \right )+\sec \left (x \right )}{-\cos \left (x \right ) x +\sin \left (x \right )}d x} \cos \left (x \right )d x \right ) c_{2} +c_{1} \right )\]