(1) Solve the following differential equations (Hint:- use Bernoulli's procedure) (i) 3(1 + x²) = 2xy(y³ − 1). (ii) y¹/2

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1 Solve The Following Differential Equations Hint Use Bernoulli S Procedure I 3 1 X 2xy Y 1 Ii Y 2 1 (41.06 KiB) Viewed 9 times

(1) Solve the following differential equations (Hint:- use Bernoulli's procedure) (i) 3(1 + x²) = 2xy(y³ − 1). (ii) y¹/2+³/2 = 1 y(0) = 4. dy dx - da (2) Solve the following differential equations (Hint:- use Ricatti's technique) dy (₂) =e² + (1+2e³)y + y², y₁=-e². (ii) y = 1-2-y+ry², y₁=1. dx (3) When interest is compounded continuously the amount of money S increase at a rate proportional to the amount present at any time: dS/dt = rS, where r is the annual rate of interest. (a) Find the amount of money accrued at the end of 5 years when AED5000 is deposited 3 in a saving account drawing 5-% annual interest compounded continuously. 4 (b) In how many years will the initial sum deposited be doubled? (c) Use a hand calculator to compare the number obtained in part (a) with the value 5(4) S=5000 + 0.0575 4 (1) This value represents the amount that would be accrued when the interest is compounded quarterly.