If person A does a work in 20 days and person B does the work in 30 days, in how many days both together complete the work?

The problem can be solved using the unitary method. The solution is: Person A does 1/20 of the work in 1 day. Person B does 1/30 of the work in 1 day Therefore they together can work at a rate of (1/20 + 1/30 = 5/60 = 1/12) work per day So, to complete 1 work together they will need = 1 / (1/12) = 12 days

what is the difference between definite and indefinite integrals?

In Indefinite integrals, we do not have the limits of the integral specified so while integrating we add a constant of integration to the answer while indefinite integrals, the limits of integration are specified and hence there is no constant of integration as the answer is evaluated at the two limits. ( Answer = Integral at upper limit - Integral at lower limit )

what is the general solution of the differential equation $ d2y/dx2 + 4y = 0 $ ?

When we have a 2nd order differential term in the equation and no first order term and a term dependent on y then the general solution is of the form y = c1 sin 2x + c2 cos 2x where the 2 in 2x term comes by taking square root of the coefficient of y in the original differential equation i.e. 4 in this case