3.162   ODE No. 162

$$\boxed{{\displaystyle (x-a)(x-b)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+{\left(y\left(x\right)\right)}^2+k(y\left(x\right)+x-a)(y\left(x\right)+x-b)=0}}$$

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

Mathematica: cpu = 0.260533 (sec), leaf count = 133 $$\left\{\{y(x)\to \frac{1}{2}\sqrt{\frac{-a^2{k}^2+2ab{k}^2-b^2{k}^2}{(k+1{)}^2}}\tan (\frac{(k+1)\sqrt{\frac{-a^2{k}^2+2ab{k}^2-b^2{k}^2}{(k+1{)}^2}}(\log (x-b)-\log (x-a))}{2(a-b)}+c_1)-\frac{-ak-bk+2kx}{2(k+1)}\}\right\}$$

Maple: cpu = 0.125 (sec), leaf count = 128 $$\{y\left(x\right)=\frac{k}{k+1}(\frac{\mathit{\_}\mathit{C}\mathit{1}{(a-x)}^{k}a}{\mathit{\_}\mathit{C}\mathit{1}{(a-x)}^k+{(b-x)}^k}-\frac{\mathit{\_}\mathit{C}\mathit{1}{(a-x)}^{k}x}{\mathit{\_}\mathit{C}\mathit{1}{(a-x)}^k+{(b-x)}^k}+\frac{{(b-x)}^{k}b}{\mathit{\_}\mathit{C}\mathit{1}{(a-x)}^k+{(b-x)}^k}-\frac{{(b-x)}^{k}x}{\mathit{\_}\mathit{C}\mathit{1}{(a-x)}^k+{(b-x)}^k})\}$$