2.1676   ODE No. 1676

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

$$a{(x{y}^{\prime }(x)-y(x))}^2-b{x}^2+x^2{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.290229 (sec), leaf count = 134

$$\left\{\{y(x)\to x({\int }_1^x\frac{i\sqrt{a}\sqrt{b}{Y}_1(-i\sqrt{a}\sqrt{b}K[2])-i\sqrt{a}\sqrt{b}{J}_1(i\sqrt{a}\sqrt{b}K[2])c_1}{a(Y_0(-i\sqrt{a}\sqrt{b}K[2])+J_0(i\sqrt{a}\sqrt{b}K[2])c_1)K[2]}dK[2]+c_2)\}\right\}$$ ✓ Maple : cpu = 0.504 (sec), leaf count = 72

$$\{y\left(x\right)=(\int -\frac{1}{ax}\sqrt{-ab}(\mathit{\_}\mathit{C}\mathit{1}{\mathit{Y}}_1\left(\sqrt{-ab}x\right)+{\mathit{J}}_1\left(\sqrt{-ab}x\right)){(\mathit{\_}\mathit{C}\mathit{1}{\mathit{Y}}_0\left(\sqrt{-ab}x\right)+{\mathit{J}}_0\left(\sqrt{-ab}x\right))}^{-1}\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{2})x\}$$