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In this paper, we investigate the pointwise time analyticity of threedifferential equations. They are the biharmonic heat equation, the heatequation with potentials and some nonlinear heat equations with powernonlinearity of order $p$. The potentials include all the nonnegative ones. Forthe first two equations, we prove if $u$ satisfies some growth conditions in$(x,t)\in \mathrm{M}\times [0,1]$, then $u$ is analytic in time $(0,1]$. Here$\mathrm{M}$ is $R^d$ or a complete noncompact manifold with Ricci curvaturebounded from below by a constant. Then we obtain a necessary and sufficientcondition such that $u(x,t)$ is analytic in time at $t=0$. Applying thismethod, we also obtain a necessary and sufficient condition for the solvabilityof the backward equations, which is ill-posed in general.  For the nonlinear heat equation with power nonlinearity of order $p$, weprove that a solution is analytic in time $t\in (0,1]$ if it is bounded in$\mathrm{M}\times[0,1]$ and $p$ is a positive integer. In addition, weinvestigate the case when $p$ is a rational number with a stronger assumption$0<C_3 \leq |u(x,t)| \leq C_4$. It is also shown that a solution may not beanalytic in time if it is allowed to be $0$. As a lemma, we obtain an estimateof $\partial_t^k \Gamma(x,t;y)$ where $\Gamma(x,t;y)$ is the heat kernel on amanifold, with an explicit estimation of the coefficients.  An interesting point is that a solution may be analytic in time even if it isnot smooth in the space variable $x$, implying that the analyticity of spaceand time can be independent. Besides, for general manifolds, space analyticitymay not hold since it requires certain bounds on curvature and its derivatives.

Time analyticity of the biharmonic heat equation, the heat equation with potentials and some nonlinear heat equations