2.1072   ODE No. 1072

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

$$y(x)(-4anp(x{)}^2+a+bp(x))+a{p}^{″}(x)y^{\prime }(x)+y^{″}(x)=0$$ ✗ Mathematica : cpu = 0.304841 (sec), leaf count = 0 , could not solve

DSolve[(a + b*p[x] - 4*a*n*p[x]^2)*y[x] + a*Derivative[1][y][x]*Derivative[2][p][x] + Derivative[2][y][x] == 0, y[x], x]

✗ Maple : cpu = 0. (sec), leaf count = 0 , result contains DESol

$$\{y\left(x\right)=\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)+a\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}p\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}\mathit{\_}\mathit{Y}\left(x\right)+(a+bp\left(x\right)-4na{\left(p\left(x\right)\right)}^2)\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\}$$