3.208   ODE No. 208

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

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

Mathematica: cpu = 0.064508 (sec), leaf count = 118 $$\{\{y(x)\to -\frac{\sqrt{4a^2{c}_1{e}^{-2ax}+4ab\cos (c+x)+c_1{e}^{-2ax}+2b\sin (c+x)}}{\sqrt{4a^2+1}}\},\{y(x)\to \frac{\sqrt{4a^2{c}_1{e}^{-2ax}+4ab\cos (c+x)+c_1{e}^{-2ax}+2b\sin (c+x)}}{\sqrt{4a^2+1}}\}\}$$

Maple: cpu = 0.047 (sec), leaf count = 116 $$\{y\left(x\right)=\frac{1}{4a^2+1}\sqrt{(4a^2+1)(4{\mathrm{e}}^{-2ax}\mathit{\_}\mathit{C}\mathit{1}{a}^2+4\cos (x+c)ab+{\mathrm{e}}^{-2ax}\mathit{\_}\mathit{C}\mathit{1}+2\sin (x+c)b)},y\left(x\right)=-\frac{1}{4a^2+1}\sqrt{(4a^2+1)(4{\mathrm{e}}^{-2ax}\mathit{\_}\mathit{C}\mathit{1}{a}^2+4\cos (x+c)ab+{\mathrm{e}}^{-2ax}\mathit{\_}\mathit{C}\mathit{1}+2\sin (x+c)b)}\}$$