3.106   ODE No. 106

$$\boxed{{\displaystyle x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+x^a{\left(y\left(x\right)\right)}^2+1/2(a-b)y\left(x\right)+x^b=0}}$$

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

Mathematica: cpu = 0.036505 (sec), leaf count = 40 $$\left\{\{y(x)\to -x^{\frac{b-a}{2}}\tan (\frac{2x^{\frac{a+b}{2}}}{a+b}-c_1)\}\right\}$$

Maple: cpu = 0.046 (sec), leaf count = 42 $$\{y\left(x\right)=-1\tan \left(\frac{1}{a+b}(\mathit{\_}\mathit{C}\mathit{1}a+\mathit{\_}\mathit{C}\mathit{1}b+2x^{a/2+b/2})\right){\left(x^{\frac{a}{2}-\frac{b}{2}}\right)}^{-1}\}$$