Solution for the Differential Equation

[nados29]

Hi,
I have a problem that I can't solve. Please help me.

Here is it:
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Verify that the function y = -(cos x) ln (sec x + tan x) is an explicit solution of the differential equation y'' + y = tan x. Assume an appropriate interval I of definition.
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First of all, I don't understand the meaning of "Assume an appropriate interval I of definition".

Second, I tried to differnetiate y = -(cos x) ln (sec x + tan x) twice in order to get y'' and replace it in the function but I couldn't. It's really difficult and terribly long. I think I'm doing it in the wrong way. Please help me in that.

Thanks.

 

[dextercioby]

The interval part is put there for you not,as not to worry about singularity points (and points in which the argument of the natural logarithm is negative) and simply do what you already did,viz.differentiate.So do not worry.Simply compute the second order derivative,even if ugly...

Daniel.

 

[Crosson]

The derivative of ln (sec + tan) is just sec.