solution to $\tan(\frac{t-s}{2}).(v_t-v_s)=0$?

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I end ep with the canonical form of the a PDE as: $$\tan(\frac{t-s}{2}).(v_t-v_s)=0$$ then I am about to find the general solution: $$v_t=v_s \iff ds=dt \iff s=t+c$$ Is it true?