2.1472   ODE No. 1472

\[ f(x) \left (x^2 y''(x)-2 x y'(x)+2 y(x)\right )+y^{(3)}(x)=0 \] Mathematica : cpu = 0.0924054 (sec), leaf count = 88


\[\left \{\left \{y(x)\to c_3 x \left (\int _1^x\frac {\exp \left (-\int _1^{K[2]}f(K[1]) K[1]^2dK[1]\right )}{K[2]^2}dK[2]-x \int _1^x\frac {\exp \left (-\int _1^{K[3]}f(K[1]) K[1]^2dK[1]\right )}{K[3]^3}dK[3]\right )+c_2 x^2+c_1 x\right \}\right \}\] Maple : cpu = 0.143 (sec), leaf count = 33


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