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using an integrating factor, find the general solution of the differential equation dy/dx +y(tanx)=tan^3(x)sec(x)

This is a first order differential equation, but initially it is not solvable as both the X&Y's can't be separated from eachother directly. An integrating factor is a specific value that when multiplied ...
TR
6109 Views

Solve (z-i)+(z+i)+(z-1)+(z-1)

Since we are dealing with complex numbers and taking its modulus, we can rewrite (z-i)=((-1)(i-z))=(i-z) doing the same for (z-1)=(1-z) we get (i-z)+(z+i)+(1-z)+(z-1)=(i+i+z-z+1+1+z-z) =(2i+2)=4 as we are ta...
YZ
4521 Views

For f(x) = (3x+4)^(-2), find f'(x) and f''(x) and hence write down the Maclaurin series up to and including the term in x^2.

f'(x)=-2(3x+4)^(-3) * 3 = -6(3x+4)^(-3); f''(x)= 18(3x+4)^(-4) * 3 = 54(3x+4)^(-4); both found by using the chain rule for differentiation. Then Maclaurin series up to x^2 is: f(x)=f(0)+f'(0)x+1/2 f''(0)x^2;...
JM
4299 Views

How do I solve x^2 + x - 6 > 0 ?

This thing we have to solve is an inequality and the solution we are looking for is an entire range of real number, something like "every x between 1 and 2", for example. To do this we need to buil...
SG
12203 Views

Integrate xcos(x) with respect to x

Using LATEX (Logarithms, Algebra, Trigonometry, Exponential and Complex numbers) to determine which variable is du and which is dv/dx. This is decided by using the above acronym. For example in this question...
VP
3214 Views