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General solution of differential equation dy/dx + tan x tan y = cos x sec y is
- a)siny = (x + c) cos x
- b)sin y = (x + c) sin y
- c)sin x = (x + c) sin y
- d)cos y = (x + c) sin x
Correct answer is option 'A'. Can you explain this answer?
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General solution of differential equation dy/dx+ tan x tan y = cos x s...
Given differential equation:
dy/dx * tan(x) * tan(y) = cos(x) * sec(y)
To find the general solution of this differential equation, we can use the method of separation of variables.
Step 1: Separate the variables
We can rewrite the equation as:
sec(y) * tan(y) dy = cos(x) * tan(x) dx
Step 2: Integrate both sides
Integrating both sides of the equation will give us:
∫sec(y) * tan(y) dy = ∫cos(x) * tan(x) dx
To integrate the left side, we can use the substitution u = tan(y), so du = sec^2(y) dy:
∫1/u du = ∫cos(x) * tan(x) dx
Step 3: Evaluate the integrals
Integrating both sides will give us:
ln|u| = ln|cos(x)| + ln|C|
where C is the constant of integration.
Step 4: Substitute back
Substituting u = tan(y) back into the equation gives us:
ln|tan(y)| = ln|cos(x)| + ln|C|
Step 5: Simplify and exponentiate
Taking the exponential of both sides will cancel out the natural logarithm:
tan(y) = C * cos(x)
Step 6: Solve for y
To solve for y, we take the inverse tangent of both sides:
y = atan(C * cos(x))
Step 7: Finalize the solution
Therefore, the general solution of the given differential equation is:
y = atan(C * cos(x)) + nπ
where C is an arbitrary constant and n is any integer.
dy/dx * tan(x) * tan(y) = cos(x) * sec(y)
To find the general solution of this differential equation, we can use the method of separation of variables.
Step 1: Separate the variables
We can rewrite the equation as:
sec(y) * tan(y) dy = cos(x) * tan(x) dx
Step 2: Integrate both sides
Integrating both sides of the equation will give us:
∫sec(y) * tan(y) dy = ∫cos(x) * tan(x) dx
To integrate the left side, we can use the substitution u = tan(y), so du = sec^2(y) dy:
∫1/u du = ∫cos(x) * tan(x) dx
Step 3: Evaluate the integrals
Integrating both sides will give us:
ln|u| = ln|cos(x)| + ln|C|
where C is the constant of integration.
Step 4: Substitute back
Substituting u = tan(y) back into the equation gives us:
ln|tan(y)| = ln|cos(x)| + ln|C|
Step 5: Simplify and exponentiate
Taking the exponential of both sides will cancel out the natural logarithm:
tan(y) = C * cos(x)
Step 6: Solve for y
To solve for y, we take the inverse tangent of both sides:
y = atan(C * cos(x))
Step 7: Finalize the solution
Therefore, the general solution of the given differential equation is:
y = atan(C * cos(x)) + nπ
where C is an arbitrary constant and n is any integer.
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General solution of differential equation dy/dx+ tan x tan y = cos x s...
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General solution of differential equation dy/dx+ tan x tan y = cos x sec y isa)siny = (x + c) cos xb)sin y = (x + c) sin yc)sin x = (x + c) sin yd)cos y = (x + c) sin xCorrect answer is option 'A'. Can you explain this answer?
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General solution of differential equation dy/dx+ tan x tan y = cos x sec y isa)siny = (x + c) cos xb)sin y = (x + c) sin yc)sin x = (x + c) sin yd)cos y = (x + c) sin xCorrect answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about General solution of differential equation dy/dx+ tan x tan y = cos x sec y isa)siny = (x + c) cos xb)sin y = (x + c) sin yc)sin x = (x + c) sin yd)cos y = (x + c) sin xCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for General solution of differential equation dy/dx+ tan x tan y = cos x sec y isa)siny = (x + c) cos xb)sin y = (x + c) sin yc)sin x = (x + c) sin yd)cos y = (x + c) sin xCorrect answer is option 'A'. Can you explain this answer?.
General solution of differential equation dy/dx+ tan x tan y = cos x sec y isa)siny = (x + c) cos xb)sin y = (x + c) sin yc)sin x = (x + c) sin yd)cos y = (x + c) sin xCorrect answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about General solution of differential equation dy/dx+ tan x tan y = cos x sec y isa)siny = (x + c) cos xb)sin y = (x + c) sin yc)sin x = (x + c) sin yd)cos y = (x + c) sin xCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for General solution of differential equation dy/dx+ tan x tan y = cos x sec y isa)siny = (x + c) cos xb)sin y = (x + c) sin yc)sin x = (x + c) sin yd)cos y = (x + c) sin xCorrect answer is option 'A'. Can you explain this answer?.
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General solution of differential equation dy/dx+ tan x tan y = cos x sec y isa)siny = (x + c) cos xb)sin y = (x + c) sin yc)sin x = (x + c) sin yd)cos y = (x + c) sin xCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for General solution of differential equation dy/dx+ tan x tan y = cos x sec y isa)siny = (x + c) cos xb)sin y = (x + c) sin yc)sin x = (x + c) sin yd)cos y = (x + c) sin xCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of General solution of differential equation dy/dx+ tan x tan y = cos x sec y isa)siny = (x + c) cos xb)sin y = (x + c) sin yc)sin x = (x + c) sin yd)cos y = (x + c) sin xCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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