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Find the general solution to the differential equation d^2x/dt^2 + 5 dx/dt + 6x = 4 e^-t

To solve a linear second order differential equation we first find the complementary function and then the particular integral. To find the complementary function we must find the roots of the auxiliary equa...
TM
8677 Views

How do I draw any graph my looking at its equation?

As graphs get more complicated I like to follow a few steps to make sure my graph looks as accurate as possible. Are there x values that make the equation (y value) get Big ? If for example I have 1/(x-2), a...
JD
3339 Views

How do I find the square root of a complex number?

Say you want to find the square root of the complex number 3+2i. We can assume that the answer we want will be in the form a+bi. It follows then, that you can also write 3+2i as (a+bi) 2 . Expanding this giv...
DC
10145 Views

Given y=arctan(3e^2x). Show dy/dx= 3/(5cosh(2x) + 4sinh(2x))

As we cannot immediately differentiate inverse tan we take tan of both sides giving us tan(y)=3e 2x. We then differentiate with respect to x, however this must be done using implicit differentiation on the l...
MS
6570 Views

A block of mass 50kg resting on a rough surface with a coefficient of friction equal to 1/3. Find the maximum angle at which the surface can be inclined to the horizontal without the block slipping. Give your answer to 3 significant figures

Break the solution down into small logical steps, outlining thought process in each one to make it clear to the examiner what it is you are try to do. Emphasise the importance of a clear and neat layout of t...
SF
4126 Views