Explanation Given information: The provided differential equation is ( 3 x − y ) d x + ( x + 3 y ) d y = 0 . Concept used: The differential equation of the form, d y d x = f ( y x ) is said to be homogeneous. And we solve it by taking v = y x . The general solution is given by, d v f ( v ) − v = d x x . Consider provided the differential equation ( 3 x − y ) d x + ( x + 3 y ) d y = 0 . The above differential equation can be written as, ( 3 x − y ) d x + ( x + 3 y ) d y = 0 d y d x = − ( 3 x − y ) ( x + 3 y ) d y d x = − ( 3 − y x ) ( 1 + 3 ( y x ) ) Now put v = y x ,then d y d x = − ( 3 − v ) ( 1 + 3 ( v ) ) = v − 3 1 + 3 v Let f ( v ) = v − 3 1 + 3 v , then we get d v f ( v ) − v = d x x d v ( v − 3 1 + 3 v ) − v = d x x ( 1 + 3 v ) d v − 3 − 3 v 2 = d x x Now integrate on both sides,

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 14.1, Problem 13PS

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That the differential equation (3x−y)dx+(x+3y)dy=0 is homogeneous and find the general solution.

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Chapter 14.1, Problem 12PS

Chapter 14.1, Problem 14PS

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That the differential equation ( 3 x − y ) d x + ( x + 3 y ) d y = 0 is homogeneous and find the general solution.

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That the differential equation (3x−y)dx+(x+3y)dy=0 is homogeneous and find the general solution.

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