Differential Eqs 1[1]

Differential Eqs 1[1] - ( 29 s k dt d --= where is the...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
205FOE102 Further Mathematics 1 Differential Equations 1 Direct Integration 1. Find the general solutions of the differential equations. (a) 1 2 - = x dx dy (b) x x dx dy - = sin (c) 2 1 x e dx dy x - = Separation of Variables 2. Find the general solutions of the differential equations. (a) ( 29 ( 29 1 1 - - = y x dx dy (b) y dx dy x y 4 2 = - (c) xy y dx dy x 3 - = 3. Solve the following boundary value problems. (a) 0 2 2 = + dx dy y x , y = 3 when x = 0 (b) 0 cos 1 = + dx dy y e x , ( 29 3 0 π = y (c) x xy dx dy y 4 2 + = , ( 29 0 0 = y 4. Solve the following initial value problems. (a) 2 cos z t dt dz = , ( 29 1 0 = z (b) u dt du t 4 2 = , u = 2 when t = 1 (c) ( 29 ( 29 1 1 + = - v v dt dv t t , ( 29 2 2 = v
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
5. Newton’s Law of Cooling states that the rate of decrease of temperature of a body is directly proportional to the difference in temperature between the body and the surroundings. This is modelled by the differential equation
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ( 29 s k dt d --= where is the temperature at time t s is the constant temperature of the surroundings k is a constant Solve this equation given that the initial temperature was = . Sketch the variation of temperature with time. 6. A chemical reaction is governed by the differential equation ( 29 2 3 x K dt dx-= where x is the concentration of chemical at time t and K is the reaction rate constant. Solve the differential equation given that the concentration is zero initially. At time t = 5, the concentration is found to be x = 1. Calculate the reaction rate constant, K . What is the final value of the concentration?...
View Full Document

Page1 / 2

Differential Eqs 1[1] - ( 29 s k dt d --= where is the...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online