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Integrating factor of differential equation cos x dy/dx+y sin x = 1 is
- a)cos x
- b)tan x
- c)sec x
- d)sin x
Correct answer is option 'C'. Can you explain this answer?
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Integrating factor of differential equation cos x dy/dx+y sin x = 1 is...
Solution:
The given differential equation is
cos x dy/dx + y sin x = 1
We need to find the integrating factor of this differential equation.
Integrating factor:
Let I be the integrating factor.
Multiplying both sides of the differential equation by I, we get
I cos x dy/dx + I y sin x = I
We know that the product rule of differentiation states that
(d/dx)(I y) = I dy/dx + y dI/dx
Comparing this with the above equation, we get
dI/dx = I sin x
Separating the variables, we get
dI/I = sin x dx
Integrating both sides, we get
ln |I| = -cos x + C
where C is the constant of integration.
Taking exponential on both sides, we get
|I| = e^(-cos x+C) = e^C e^(-cos x)
Since e^C is a positive constant, we can write
I = ± e^(-cos x)
However, we need to choose the positive sign since the integrating factor should be positive.
Therefore, the integrating factor of the given differential equation is
I = e^(-cos x) = sec x
Hence, Option C is the correct answer.
The given differential equation is
cos x dy/dx + y sin x = 1
We need to find the integrating factor of this differential equation.
Integrating factor:
Let I be the integrating factor.
Multiplying both sides of the differential equation by I, we get
I cos x dy/dx + I y sin x = I
We know that the product rule of differentiation states that
(d/dx)(I y) = I dy/dx + y dI/dx
Comparing this with the above equation, we get
dI/dx = I sin x
Separating the variables, we get
dI/I = sin x dx
Integrating both sides, we get
ln |I| = -cos x + C
where C is the constant of integration.
Taking exponential on both sides, we get
|I| = e^(-cos x+C) = e^C e^(-cos x)
Since e^C is a positive constant, we can write
I = ± e^(-cos x)
However, we need to choose the positive sign since the integrating factor should be positive.
Therefore, the integrating factor of the given differential equation is
I = e^(-cos x) = sec x
Hence, Option C is the correct answer.
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Integrating factor of differential equation cos x dy/dx+y sin x = 1 isa)cos xb)tan xc)sec xd)sin xCorrect answer is option 'C'. Can you explain this answer?
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Integrating factor of differential equation cos x dy/dx+y sin x = 1 isa)cos xb)tan xc)sec xd)sin xCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Integrating factor of differential equation cos x dy/dx+y sin x = 1 isa)cos xb)tan xc)sec xd)sin xCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Integrating factor of differential equation cos x dy/dx+y sin x = 1 isa)cos xb)tan xc)sec xd)sin xCorrect answer is option 'C'. Can you explain this answer?.
Integrating factor of differential equation cos x dy/dx+y sin x = 1 isa)cos xb)tan xc)sec xd)sin xCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Integrating factor of differential equation cos x dy/dx+y sin x = 1 isa)cos xb)tan xc)sec xd)sin xCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Integrating factor of differential equation cos x dy/dx+y sin x = 1 isa)cos xb)tan xc)sec xd)sin xCorrect answer is option 'C'. Can you explain this answer?.
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