ODE No. 1471

\[ f(x) y''(x)+f(x) y(x)+y^{(3)}(x)+y'(x)=0 \] Mathematica : cpu = 0.0778437 (sec), leaf count = 84

DSolve[f[x]*y[x] + Derivative[1][y][x] + f[x]*Derivative[2][y][x] + Derivative[3][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_3 e^{i x} \int _1^xe^{-2 i K[3]} \int _1^{K[3]}\exp \left (\int _1^{K[2]}(i-f(K[1]))dK[1]\right )dK[2]dK[3]+c_1 e^{i x}+\frac {1}{2} i c_2 e^{-i x}\right \}\right \}\] Maple : cpu = 0.143 (sec), leaf count = 36

dsolve(diff(diff(diff(y(x),x),x),x)+f(x)*diff(diff(y(x),x),x)+diff(y(x),x)+f(x)*y(x)=0,y(x))
 

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