1. (a) Solve the following first order differential equations by using the appropriate method. i. 2xdx - ydy = 0, write

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1 A Solve The Following First Order Differential Equations By Using The Appropriate Method I 2xdx Ydy 0 Write 1 (86.31 KiB) Viewed 22 times

1. (a) Solve the following first order differential equations by using the appropriate method. i. 2xdx - ydy = 0, write your answer in the form y = f(x). dy ii. +y = sinx, y(t) = 1. dx (10 marks) (b) A certain radioactive material in known to decay at the rate propo- tional to the amount present. If initially there is 100 miligrams of the material present and after two hours it is observed that the material has lost 10 percent of its original mass. By using growth dx population formula, =kx, find dt i. an expression for the mass of the material remaining at any time t. ii. the mass of the material after five hours. iii. the time at which the material has decayed to one half of its initial mass. (10 marks)