2.1080   ODE No. 1080

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ y(x) \left (a^2+\frac {a f'(x)}{f(x)}-b^2 f(x)^2\right )-y'(x) \left (2 a+\frac {f'(x)}{f(x)}\right )+y''(x)=0 \] Mathematica : cpu = 0.0665177 (sec), leaf count = 49

\[\left \{\left \{y(x)\to c_1 \exp \left (b \int _1^xf(K[1])dK[1]+a x\right )+c_2 \exp \left (a x-b \int _1^xf(K[2])dK[2]\right )\right \}\right \}\] Maple : cpu = 0.577 (sec), leaf count = 74

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