2.1658   ODE No. 1658

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

$$y^{″}(x)-h(y^{\prime }(x),ax+by(x))=0$$ ✗ Mathematica : cpu = 0.120271 (sec), leaf count = 0 , could not solve

DSolve[-h[Derivative[1][y][x], a*x + b*y[x]] + Derivative[2][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.146 (sec), leaf count = 115

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