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By using an integrating factor, solve the differential equation dy/dx + 4y/x = 6x^-3 (6 marks)

Answer : y = 3/x 2 + c/x 4 Integrating factor is 4/x (1 mark) => I = e integral (4/x) dx (1 mark) => I = x 4 (1 mark) . Using the formula, d/dx (x 4 y) = 6x (1 mark) => x 4 y = integral(6x)dx (1 mar...
MD
7194 Views

I don't understand how proof by mathematical induction works, can you help?

This took me some time to get my head around so I know what you mean. I always like to think of proof by induction like dominoes. Once you've pushed the first domino in line of dominos, you know it's going t...
JB
2766 Views

Solve the following complex equation: '(a + b)(2 + i) = b + 1 + (10 + 2a)i' to find values for 'a' and 'b'

The first step with this question is to expand all the brackets; this will produce the following equation: 2a + ai + 2b + bi = b + 1 + 10i + 2ai The next step is to put all the terms which contain what you'r...
SM
15707 Views

Find the general solution of the differential equation d^2y/dx^2 - 5*dy/dx + 4y = 2x

Solve complimentary function: Let y = e mx then, d 2 y/dx 2 - 5dy/dx + 4y = 0 m 2 e mx - 5me mx + 4e mx = 0 (substituting for y) e mx (m 2 - 5m + 4) = 0 e mx (m - 4)(m - 1) = 0 Therefore m=4 and m=1, so the ...
PM
13763 Views

In simple harmonic motion, where would the object have the largest speed. If the angular velocity is 2 rad s^-1, and the amplitude is 1m, what is the largest speed obtained by the object?

The largest speed is obtained at the position of equilibrium. v=Aw So v= 2 x 1 v=2ms -1
WC
3240 Views