Question

Write a differential equation describing a second order reaction – a reaction in
which the rate of depletion of the concentration of the reactants depends on the
square of reactants’ concentration. Solve this differential equation and hence find
an expression for the concentration of the reactants as a function of time.

Have you looked in your text for this. I think I have a freshman text that lists the integrated equation.
No, I can't find one for a second order reaction.
For the reaction
aA ==>products.
d[A]/adt = k[A]^2

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