2.1029   ODE No. 1029

\[ y''(x)-y(x) \left (f'(x)+f(x)^2\right )=0 \]

✓ Mathematica : cpu = 0.0178158 (sec), leaf count = 58

DSolve[-(y[x]*(f[x]^2 + Derivative[1][f][x])) + Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 \exp \left (\int _1^xf(K[1])dK[1]\right )+c_2 \exp \left (\int _1^xf(K[2])dK[2]\right ) \int _1^x\exp \left (\int _1^{K[4]}-2 f(K[3])dK[3]\right )dK[4]\right \}\right \}\]

✓ Maple : cpu = 0.184 (sec), leaf count = 22

dsolve(diff(diff(y(x),x),x)-(f(x)^2+diff(f(x),x))*y(x)=0,y(x))
 

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