Chapter 12: Q. 66 (page 945)

Solve the exact differential equations in Exercises 63–66. $\frac{12 x^{3}}{y^{5}} - \frac{15 x^{4}}{y^{6}} \frac{d y}{d x} = 0 .$

Short Answer

Expert verified

The solution of given exact differential equation is: $\frac{3 x^{4}}{y^{5}} + C = 0$

Step by step solution

Step 1. Given information

Exact differential equation, $\frac{12 x^{3}}{y^{5}} - \frac{15 x^{4}}{y^{6}} \frac{d y}{d x} = 0$

Step 2. Solving the given exact differential equation

$Given, \frac{12 x^{3}}{y^{5}} - \frac{15 x^{4}}{y^{6}} \frac{d y}{d x} = 0 \Rightarrow \frac{12 x^{3}}{y^{5}} d x - \frac{15 x^{4}}{y^{6}} d y = 0 It is a exact differential equation of the the form M d x + N d y = 0, with \frac{\partial M}{\partial y} = \frac{\partial N}{\partial x} . the solution is given by, f (x, y) = \int (treating y a s constant in M) d x + \int (terms independent of x in N) d y = 0 \Rightarrow \int \frac{12 x^{3}}{y^{5}} d x - \int (0) d y = 0 \Rightarrow \frac{12 x^{4}}{4 y^{5}} + C = 0 \Rightarrow \frac{3 x^{4}}{y^{5}} + C = 0$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve the exact differential equations in Exercises 63–66. $\frac{12 x^{3}}{y^{5}} - \frac{15 x^{4}}{y^{6}} \frac{d y}{d x} = 0 .$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving the given exact differential equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

Solve the exact differential equations in Exercises 63–66.12x3y5−15x4y6dydx=0.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving the given exact differential equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

Solve the exact differential equations in Exercises 63–66. $\frac{12 x^{3}}{y^{5}} - \frac{15 x^{4}}{y^{6}} \frac{d y}{d x} = 0 .$