3.180   ODE No. 180

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

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

Mathematica: cpu = 0.123016 (sec), leaf count = 132 $$\left\{\{y(x)\to -\frac{x(\exp (\frac{4{\tan }^{-1}(\frac{2ax}{\sqrt{4ac-b^2}}+\frac{b}{\sqrt{4ac-b^2}})}{\sqrt{4ac-b^2}}+2c_1)-1)}{\exp (\frac{4{\tan }^{-1}(\frac{2ax}{\sqrt{4ac-b^2}}+\frac{b}{\sqrt{4ac-b^2}})}{\sqrt{4ac-b^2}}+2c_1)+1}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 58 $$\{y\left(x\right)=-\tanh \left(1(\mathit{\_}\mathit{C}\mathit{1}\sqrt{4ac-b^2}+2\arctan \left(\frac{2ax+b}{\sqrt{4ac-b^2}}\right))\frac{1}{\sqrt{4ac-b^2}}\right)x\}$$