2.331   ODE No. 331

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

$$y^{\prime }(x)(\sum _{\nu =1}^{p}y(x{)}^{\nu }f(\nu )(x))-\sum _{\nu =1}^{q}y(x{)}^{\nu }g(\nu )(x)=0$$ ✗ Mathematica : cpu = 55.8894 (sec), leaf count = 0 , could not solve

DSolve[-Sum[y[x]^nu*g[nu][x], {nu, 1, q}] + Sum[y[x]^nu*f[nu][x], {nu, 1, p}]*Derivative[1][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.241 (sec), leaf count = 78

$$\{\frac{y{\left(x\right)}^{p+1}\mathrm{\Phi }(-{(-1)}^{\mathrm{csgn}\left(iy{\left(x\right)}^q\right)}y{\left(x\right)}^q,1,\frac{p+1}{q})-y\left(x\right)\mathrm{\Phi }(-{(-1)}^{\mathrm{csgn}\left(iy{\left(x\right)}^q\right)}y{\left(x\right)}^q,1,\frac{1}{q})+(c_1+\int \frac{g_{\nu }\left(x\right)}{f_{\nu }\left(x\right)}dx)q}{q}=0\}$$