FP2 First Oder Differential Equation Help

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brawlerpit
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#1
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#1
Hi, I'm stuck on this question.

cosx(dy/dx) + y = 1

It's in the Edexcel FP2 book, and the excersize is solving differential equations by multiplying through an integrating factor when the equation is the in the form (dy/dx) + P(x)y = Q(x).

I tried to make the equation fit in that form by dividing through by cosx

(dy/dx) + ysec(x) = sec(x) , which implies that P(x) is sec(X) but I can't integrate e^intergrate;sec(x)dx

I'm thinking I need to make changes to the original equation first, like multiplying through by other trig functions, but that hasn't worked...:/

Thanks for the help in advance :P
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user2020user
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#2
Report 8 years ago
#2
(Original post by brawlerpit)
Question
Hi, I'm stuck on this question.

cosx(dy/dx) + y = 1

It's in the Edexcel FP2 book, and the excersize is solving differential equations by multiplying through an integrating factor when the equation is the in the form (dy/dx) + P(x)y = Q(x).

I tried to make the equation fit in that form by dividing through by cosx

(dy/dx) + ysec(x) = sec(x) , which implies that P(x) is sec(X) but I can't integrate e^intergrate;sec(x)dx

I'm thinking I need to make changes to the original equation first, like multiplying through by other trig functions, but that hasn't worked...:/

Thanks for the help in advance :P
To find \displaystyle \int \sec(x)\ dx, make the substitution u=\sec(x) + \tan(x)
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brianeverit
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#3
Report 8 years ago
#3
(Original post by brawlerpit)
Hi, I'm stuck on this question.

cosx(dy/dx) + y = 1

It's in the Edexcel FP2 book, and the excersize is solving differential equations by multiplying through an integrating factor when the equation is the in the form (dy/dx) + P(x)y = Q(x).

I tried to make the equation fit in that form by dividing through by cosx

(dy/dx) + ysec(x) = sec(x) , which implies that P(x) is sec(X) but I can't integrate e^intergrate;sec(x)dx

I'm thinking I need to make changes to the original equation first, like multiplying through by other trig functions, but that hasn't worked...:/

Thanks for the help in advance :P
Multiply by  \frac{\sec x+\tan x}{\sec x+\tan x} and note that the numerator is then the derivative of the denominator
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