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Find the general solution the the differential equation question.

image.jpg
Hey the question and my working is in the image above. (question e)
Where did I go wrong .
Thanks.
(edited 8 years ago)
Reply 1
Hi

I've just tried this question and am getting the same thing that you got,except doesn't e^c just become a constant A. So isn't it x+A not Ax? Do you have the answer?
Reply 2
Original post by Zebash04
Hi

I've just tried this question and am getting the same thing that you got,except doesn't e^c just become a constant A. So isn't it x+A not Ax? Do you have the answer?


Sorry I've realised I've done ti wrong as well :biggrin: It should be Ax. Are you sure your answer isn't right?
You get

ln(secy)=ln(x)+csecy=elnx+c=Ax\ln (\sec y) = \ln(x) + c \Rightarrow \sec y = e^{\ln x + c} = Ax

which is correct.

Alternatively, if you write

ln(secy)=ln(cosy)\ln (\sec y) = -\ln(\cos y)

Then

ln(cosy)=ln(1x)+c\ln (\cos y) = \ln\left(\dfrac{1}{x}\right) + c

etc etc

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