Explanation Given information: The provided differential equation is ( 2 x y 2 + 3 x 2 y − y 3 ) d x + ( 2 x 2 y + x 3 − 3 x y 2 ) 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 the provided differential equation ( 2 x y 2 + 3 x 2 y − y 3 ) d x + ( 2 x 2 y + x 3 − 3 x y 2 ) d y = 0 . The given equation can also be written as, ( 2 x y 2 + 3 x 2 y − y 3 ) d x + ( 2 x 2 y + x 3 − 3 x y 2 ) d y = 0 ( 2 ( y 2 x 2 ) + 3 ( y x ) − ( y 3 x 3 ) ) d x + ( 2 ( y x ) + 1 − 3 ( y 2 x 2 ) ) d y = 0 d y d x = − ( 2 ( y 2 x 2 ) + 3 ( y x ) − ( y 3 x 3 ) ) ( 2 ( y x ) + 1 − 3 ( y 2 x 2 ) ) Now put v = y x ,then d y d x = − ( 2 ( v 2 ) + 3 ( v ) − ( v 3 ) ) ( 2 ( v ) + 1 − 3 ( v 2 ) ) = − 2 v 2 − 3 v + v 3 2 v + 1 − 3 v 2 Let f ( v ) = − 2 v 2 − 3 v + v 3 2 v + 1 − 3 v 2 , then we get &e

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

See similar textbooks

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Videos

Question

Chapter 14.1, Problem 33PS

To determine

Whether the equation (2xy2+3x2y−y3)dx+(2x2y+x3−3xy2)dy=0 is separable, homogenous, first-order linear, or exact, and then find the solution.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.1, Problem 32PS

Chapter 14.1, Problem 34PS

Students have asked these similar questions

6. Give the equation for the following (-2, 0) y ++ + X

1)The sum of three consecutive multiples of 4 is 444. Find these multiples. [This is a problem on linear equations in one variable] 2.State the steps you will take to transform 3x + n = 7 to x = (1/3)[7- n]

2. Solve the equation cosecxcosydy - 10xdx , separably

Chapter 14 Solutions

Calculus

Ch. 14.1 - Prob. 1PS Ch. 14.1 - Prob. 2PS Ch. 14.1 - Prob. 3PS Ch. 14.1 - Prob. 4PS Ch. 14.1 - Prob. 5PS Ch. 14.1 - Prob. 6PS Ch. 14.1 - Prob. 7PS Ch. 14.1 - Prob. 8PS Ch. 14.1 - Prob. 9PS Ch. 14.1 - Prob. 10PS

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Whether the equation ( 2 x y 2 + 3 x 2 y − y 3 ) d x + ( 2 x 2 y + x 3 − 3 x y 2 ) d y = 0 is separable, homogenous, first-order linear, or exact, and then find the solution.

Solution Summary: The author explains that the differential equation (2xy2+3x

Concept explainers

Videos

Whether the equation (2xy2+3x2y−y3)dx+(2x2y+x3−3xy2)dy=0 is separable, homogenous, first-order linear, or exact, and then find the solution.

Want to see the full answer?

Chapter 14 Solutions