2.1624   ODE No. 1624

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

$$y(x)(af(x{)}^2+3f^{\prime }(x)+\frac{3f^{\prime }(x{)}^2}{f(x{)}^2}-\frac{f^{″}(x)}{f(x)})+bf(x{)}^3-(\frac{f^{\prime }(x)}{f(x)}+f(x))(3y^{\prime }(x)+y(x{)}^2)+y(x)y^{\prime }(x)+y^{″}(x)-y(x{)}^3=0$$ ✗ Mathematica : cpu = 0.62962 (sec), leaf count = 0 , could not solve

DSolve[b*f[x]^3 - y[x]^3 + y[x]*Derivative[1][y][x] - (f[x] + Derivative[1][f][x]/f[x])*(y[x]^2 + 3*Derivative[1][y][x]) + y[x]*(a*f[x]^2 + 3*Derivative[1][f][x] + (3*Derivative[1][f][x]^2)/f[x]^2 - Derivative[2][f][x]/f[x]) + Derivative[2][y][x] == 0, y[x], x]

✓ Maple : cpu = 1.872 (sec), leaf count = 131

$$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(f\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}-{\int }^{\mathit{\_}\mathit{Z}}f\left(\mathit{\_}\mathit{f}\right)d\mathit{\_}\mathit{f})\right)\mathit{\_}\mathit{a},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)={\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2((-{\mathit{\_}\mathit{a}}^3-{\mathit{\_}\mathit{a}}^2+\mathit{\_}\mathit{a}a+b)\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+\mathit{\_}\mathit{a}-3)\},\{\mathit{\_}\mathit{a}=\frac{y\left(x\right)}{f\left(x\right)},\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{{\left(f\left(x\right)\right)}^3}{f\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-\left(\frac{\mathrm{d}}{\mathrm{d}x}f\left(x\right)\right)y\left(x\right)}\},\{x=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}-{\int }^{\mathit{\_}\mathit{Z}}f\left(\mathit{\_}\mathit{f}\right)d\mathit{\_}\mathit{f}),y\left(x\right)=f\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}-{\int }^{\mathit{\_}\mathit{Z}}f\left(\mathit{\_}\mathit{f}\right)d\mathit{\_}\mathit{f})\right)\mathit{\_}\mathit{a}\}])\}$$