3.77   ODE No. 77

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-\cos (ay\left(x\right)+bx)=0}}$$

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

Mathematica: cpu = 0.318040 (sec), leaf count = 124 $$\left\{\{y(x)\to \frac{-2{\tan }^{-1}(\frac{a\tanh \left(\frac{1}{2}(c_1\sqrt{a^2-b^2}-x\sqrt{a^2-b^2})\right)}{\sqrt{a^2-b^2}}+\frac{b\tanh \left(\frac{1}{2}(c_1\sqrt{a^2-b^2}-x\sqrt{a^2-b^2})\right)}{\sqrt{a^2-b^2}})-bx}{a}\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 65 $$\{y\left(x\right)=-\frac{1}{a}(bx+2\arctan \left(\frac{\tanh (1/2\mathit{\_}\mathit{C}\mathit{1}\sqrt{a^2-b^2}-1/2x\sqrt{a^2-b^2})\sqrt{a^2-b^2}}{a-b}\right))\}$$