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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
8695 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
3359 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
10174 Views

A curve has equation: y = x^3 - 3x^2 + 5. Show that the curve has a minimum point when x = 2.

A minimum point will have a gradient of 0 (although so will a maximum point or a point of inflection). dy/dx = 3x 2 -6x. We can substitute x = 2 into this equation to give 0 (alternatively solve 3x 2 -6x = 0...
TC
9680 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
6595 Views