8.68   ODE No. 1658

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-h(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right),ax+by\left(x\right))=0}}$$

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

Mathematica: cpu = 0.130517 (sec), leaf count = 26 $$\text{DSolve}[y^{″}(x)-h(y^{\prime }(x),ax+by(x))=0,y(x),x]$$

Maple: cpu = 0.094 (sec), leaf count = 117 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(-\frac{a(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})-b\mathit{\_}\mathit{a}}{b},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-h(-\frac{a\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-b}{\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)b},b\mathit{\_}\mathit{a}){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3\},\{\mathit{\_}\mathit{a}=\frac{ax+by\left(x\right)}{b},\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{b}{a+b\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}\},\{x=\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=-\frac{a(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})-b\mathit{\_}\mathit{a}}{b}\}])\}$$