2.373   ODE No. 373

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

$$a^{2}y(x{)}^2({\log }^2(y(x))-1)+y^{\prime }(x{)}^2=0$$ ✓ Mathematica : cpu = 0.295552 (sec), leaf count = 185

$$\{\{y(x)\to \exp (-\frac{1}{2}\sqrt{-e^{2iax-2c_1}-e^{2c_1-2iax}+2})\},\{y(x)\to \exp \left(\frac{1}{2}\sqrt{-e^{2iax-2c_1}-e^{2c_1-2iax}+2}\right)\},\{y(x)\to \exp (-\frac{1}{2}\sqrt{-e^{-2iax-2c_1}-e^{2iax+2c_1}+2})\},\{y(x)\to \exp \left(\frac{1}{2}\sqrt{-e^{-2iax-2c_1}-e^{2iax+2c_1}+2}\right)\}\}$$ ✓ Maple : cpu = 0.186 (sec), leaf count = 49

$$\{y\left(x\right)={\left({\mathrm{e}}^{-\sin \left(a(x-\mathit{\_}\mathit{C}\mathit{1})\right)}\right)}^{-1},y\left(x\right)={\mathrm{e}}^{-\sin \left(a(x-\mathit{\_}\mathit{C}\mathit{1})\right)},y\left(x\right)={\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}\left(a^2{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2({\mathit{\_}\mathit{Z}}^2-1)\right)}\}$$