3.474   ODE No. 474

$$\boxed{{\displaystyle 2y\left(x\right){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-(4x-5)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+2y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.232029 (sec), leaf count = 135 $$\{\{y(x)\to -i\sqrt{2}{e}^{\frac{c_1}{2}}\sqrt{8e^{c_1}+4x-5}\},\{y(x)\to i\sqrt{2}{e}^{\frac{c_1}{2}}\sqrt{8e^{c_1}+4x-5}\},\{y(x)\to -\frac{1}{4}i{e}^{\frac{c_1}{2}}\sqrt{e^{c_1}+8x-10}\},\{y(x)\to \frac{1}{4}i{e}^{\frac{c_1}{2}}\sqrt{e^{c_1}+8x-10}\}\}$$

Maple: cpu = 1.295 (sec), leaf count = 154 $$\{\ln (x-\frac{5}{4})+\frac{1}{2}\ln (16\frac{{\left(y\left(x\right)\right)}^2}{{(4x-5)}^2}-1)-\sqrt{-16\frac{{\left(y\left(x\right)\right)}^2}{{(4x-5)}^2}+1}+\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\frac{1}{\sqrt{-16\frac{{\left(y\left(x\right)\right)}^2}{{(4x-5)}^2}+1}}\right)+\frac{\sqrt{4}}{2}\sqrt{\frac{-16{\left(y\left(x\right)\right)}^2+16x^2-40x+25}{{(4x-5)}^2}}+\ln \left(\frac{y\left(x\right)}{4x-5}\right)-\frac{1}{2}\ln (4\frac{y\left(x\right)}{4x-5}+1)-\frac{1}{2}\ln (4\frac{y\left(x\right)}{4x-5}-1)-\mathit{\_}\mathit{C}\mathit{1}=0,y\left(x\right)=-x+\frac{5}{4},y\left(x\right)=x-\frac{5}{4}\}$$