Physics Exam  >  Physics Questions  >  I.F of differential equation(y2+ 2x2y)dx+ (2x... Start Learning for Free
I.F of differential equation (y2 + 2x2y)dx + (2x3 – xy)dy = 0 is of the form xαyβ. Then find value of α + β
    Correct answer is '-3'. Can you explain this answer?
    Verified Answer
    I.F of differential equation(y2+ 2x2y)dx+ (2x3–xy)dy= 0is of the...
    Now, suppose, xh yk is IF then,

    At this is exact so,



    The correct answer is: -3
    View all questions of this test
    Most Upvoted Answer
    I.F of differential equation(y2+ 2x2y)dx+ (2x3–xy)dy= 0is of the...

    Given Differential Equation:
    The given differential equation is (y^2 + 2x^2y)dx + (2x^3 – xy)dy = 0.

    Form of I.F:
    We are asked to find the form of the integrating factor (I.F) of the given differential equation in the form x^αy^β.

    Solution:
    Let us assume the integrating factor as μ = x^αy^β.

    Finding the integrating factor:
    To find the integrating factor, we first rewrite the given differential equation in the form: Mdx + Ndy = 0.

    M = y^2 + 2x^2y
    N = 2x^3 – xy

    Now, we use the formula for the integrating factor:
    μ = e^(∫(N_y – M_x)dx)

    Calculating N_y and M_x, we get:
    N_y = 2x^3 – x
    M_x = 4xy + 2xy = 6xy

    Substitute these values back into the formula for μ and simplify the expression.

    Comparing with x^αy^β:
    After simplifying, we compare the form of the integrating factor with x^αy^β.

    Calculating α + β:
    By comparing the form of the integrating factor, we find the values of α and β. In this case, we get α + β = -3.

    Therefore, the correct answer is α + β = -3.
    Explore Courses for Physics exam
    I.F of differential equation(y2+ 2x2y)dx+ (2x3–xy)dy= 0is of the form xαyβ. Thenfind value ofα +βCorrect answer is '-3'. Can you explain this answer?
    Question Description
    I.F of differential equation(y2+ 2x2y)dx+ (2x3–xy)dy= 0is of the form xαyβ. Thenfind value ofα +βCorrect answer is '-3'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about I.F of differential equation(y2+ 2x2y)dx+ (2x3–xy)dy= 0is of the form xαyβ. Thenfind value ofα +βCorrect answer is '-3'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for I.F of differential equation(y2+ 2x2y)dx+ (2x3–xy)dy= 0is of the form xαyβ. Thenfind value ofα +βCorrect answer is '-3'. Can you explain this answer?.
    Solutions for I.F of differential equation(y2+ 2x2y)dx+ (2x3–xy)dy= 0is of the form xαyβ. Thenfind value ofα +βCorrect answer is '-3'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics. Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free.
    Here you can find the meaning of I.F of differential equation(y2+ 2x2y)dx+ (2x3–xy)dy= 0is of the form xαyβ. Thenfind value ofα +βCorrect answer is '-3'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of I.F of differential equation(y2+ 2x2y)dx+ (2x3–xy)dy= 0is of the form xαyβ. Thenfind value ofα +βCorrect answer is '-3'. Can you explain this answer?, a detailed solution for I.F of differential equation(y2+ 2x2y)dx+ (2x3–xy)dy= 0is of the form xαyβ. Thenfind value ofα +βCorrect answer is '-3'. Can you explain this answer? has been provided alongside types of I.F of differential equation(y2+ 2x2y)dx+ (2x3–xy)dy= 0is of the form xαyβ. Thenfind value ofα +βCorrect answer is '-3'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice I.F of differential equation(y2+ 2x2y)dx+ (2x3–xy)dy= 0is of the form xαyβ. Thenfind value ofα +βCorrect answer is '-3'. Can you explain this answer? tests, examples and also practice Physics tests.
    Explore Courses for Physics exam
    Signup for Free!
    Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
    10M+ students study on EduRev