2.1841   ODE No. 1841

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

$$-f(x)+x^2{y}^{(3)}(x)+x{y}^{″}(x)+(2xy(x)-1)y^{\prime }(x)+y(x{)}^2=0$$ ✗ Mathematica : cpu = 0.0868286 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 0.534 (sec), leaf count = 60

$$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right),[\{{\mathit{\_}\mathit{a}}^2\frac{{\mathrm{d}}^2}{\mathrm{d}{\mathit{\_}\mathit{a}}^2}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+\mathit{\_}\mathit{a}{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2-\mathit{\_}\mathit{a}\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-\int f\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\},\{\mathit{\_}\mathit{a}=x,\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=y\left(x\right)\},\{x=\mathit{\_}\mathit{a},y\left(x\right)=\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\}])\}$$