Mathematics Exam > Mathematics Questions > The integrating factor of the differential eq...
Start Learning for Free
The integrating factor of the differential equation (x3 + y2 + 2x)dx + 2ydy = 0 is
- a)ex
- b)e-x
- c)log x
- d)exy
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The integrating factor of the differential equation (x3 + y2+2x)dx + 2...
Hint : Here
Most Upvoted Answer
The integrating factor of the differential equation (x3 + y2+2x)dx + 2...
Given:
The given differential equation is:
(x^3 - y^2 + 2x)dx + 2ydy = 0
To find:
The integrating factor of the given differential equation.
Solution:
To find the integrating factor, we can use the following formula:
Integrating factor (IF) = e^∫P(x)dx
Step 1: Identify P(x) in the given differential equation:
The given differential equation is:
(x^3 - y^2 + 2x)dx + 2ydy = 0
Comparing this with the standard form:
M(x, y)dx + N(x, y)dy = 0
We can identify P(x) as: P(x) = x^3 - y^2 + 2x
Step 2: Find the integral of P(x):
∫P(x)dx = ∫(x^3 - y^2 + 2x)dx
Using the power rule of integration, we can find the integral:
∫x^3dx = (1/4)x^4 + C1
∫-y^2dx = -y^2x + C2
∫2xdx = x^2 + C3
So, ∫P(x)dx = (1/4)x^4 - y^2x + x^2 + C
Step 3: Find the integrating factor:
The integrating factor (IF) is given by the formula:
IF = e^∫P(x)dx
Substituting the value of ∫P(x)dx, we get:
IF = e^((1/4)x^4 - y^2x + x^2 + C)
Since C is an arbitrary constant, we can write it as:
IF = Ke^((1/4)x^4 - y^2x + x^2)
Where K is an arbitrary constant.
Thus, the integrating factor of the given differential equation is:
IF = Ke^((1/4)x^4 - y^2x + x^2)
Final Answer:
The correct option is 'A', i.e., ex.
The given differential equation is:
(x^3 - y^2 + 2x)dx + 2ydy = 0
To find:
The integrating factor of the given differential equation.
Solution:
To find the integrating factor, we can use the following formula:
Integrating factor (IF) = e^∫P(x)dx
Step 1: Identify P(x) in the given differential equation:
The given differential equation is:
(x^3 - y^2 + 2x)dx + 2ydy = 0
Comparing this with the standard form:
M(x, y)dx + N(x, y)dy = 0
We can identify P(x) as: P(x) = x^3 - y^2 + 2x
Step 2: Find the integral of P(x):
∫P(x)dx = ∫(x^3 - y^2 + 2x)dx
Using the power rule of integration, we can find the integral:
∫x^3dx = (1/4)x^4 + C1
∫-y^2dx = -y^2x + C2
∫2xdx = x^2 + C3
So, ∫P(x)dx = (1/4)x^4 - y^2x + x^2 + C
Step 3: Find the integrating factor:
The integrating factor (IF) is given by the formula:
IF = e^∫P(x)dx
Substituting the value of ∫P(x)dx, we get:
IF = e^((1/4)x^4 - y^2x + x^2 + C)
Since C is an arbitrary constant, we can write it as:
IF = Ke^((1/4)x^4 - y^2x + x^2)
Where K is an arbitrary constant.
Thus, the integrating factor of the given differential equation is:
IF = Ke^((1/4)x^4 - y^2x + x^2)
Final Answer:
The correct option is 'A', i.e., ex.
Free Test
FREE
| Start Free Test |
Community Answer
The integrating factor of the differential equation (x3 + y2+2x)dx + 2...
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
The integrating factor of the differential equation (x3 + y2+2x)dx + 2ydy =0 isa)exb)e-xc)log xd)exyCorrect answer is option 'A'. Can you explain this answer?
Question Description
The integrating factor of the differential equation (x3 + y2+2x)dx + 2ydy =0 isa)exb)e-xc)log xd)exyCorrect 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 The integrating factor of the differential equation (x3 + y2+2x)dx + 2ydy =0 isa)exb)e-xc)log xd)exyCorrect 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 The integrating factor of the differential equation (x3 + y2+2x)dx + 2ydy =0 isa)exb)e-xc)log xd)exyCorrect answer is option 'A'. Can you explain this answer?.
The integrating factor of the differential equation (x3 + y2+2x)dx + 2ydy =0 isa)exb)e-xc)log xd)exyCorrect 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 The integrating factor of the differential equation (x3 + y2+2x)dx + 2ydy =0 isa)exb)e-xc)log xd)exyCorrect 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 The integrating factor of the differential equation (x3 + y2+2x)dx + 2ydy =0 isa)exb)e-xc)log xd)exyCorrect answer is option 'A'. Can you explain this answer?.
Solutions for The integrating factor of the differential equation (x3 + y2+2x)dx + 2ydy =0 isa)exb)e-xc)log xd)exyCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of The integrating factor of the differential equation (x3 + y2+2x)dx + 2ydy =0 isa)exb)e-xc)log xd)exyCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The integrating factor of the differential equation (x3 + y2+2x)dx + 2ydy =0 isa)exb)e-xc)log xd)exyCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for The integrating factor of the differential equation (x3 + y2+2x)dx + 2ydy =0 isa)exb)e-xc)log xd)exyCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of The integrating factor of the differential equation (x3 + y2+2x)dx + 2ydy =0 isa)exb)e-xc)log xd)exyCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The integrating factor of the differential equation (x3 + y2+2x)dx + 2ydy =0 isa)exb)e-xc)log xd)exyCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup