Chapter 12: Q. 64 (page 945)

Solve the exact differential equations in Exercises 63–66. $y \cos (x y) - 3 + (x \cos (x y) + 2) \frac{d y}{d x} = 0 .$

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Expert verified

The solution of given exact differential equation is: $\sin (x y) - 3 x + 2 y + C = 0$

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Step 1. Given information

Exact differential equation, $y \cos (x y) - 3 + (x \cos (x y) + 2) \frac{d y}{d x} = 0$

Step 2. Solving the given exact differential equation

$y \cos (x y) - 3 + (x \cos (x y) + 2) \frac{d y}{d x} = 0 \Rightarrow (y \cos (x y) - 3) d x + (x \cos (x y) + 2) d y = 0 It is a exact differential equation of the the form M d x + N d y = 0, with \frac{\partial M}{\partial y} = \frac{\partial N}{\partial x} . the solution is given by, f (x, y) = \int (treating y a s constant in M) d x + \int (terms independent of x in N) d y = 0 \Rightarrow \int (y \cos (x y) - 3) d x + \int (2) d y = 0 \Rightarrow \sin (x y) - 3 x + 2 y + C = 0$

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Solve the exact differential equations in Exercises 63–66. $y \cos (x y) - 3 + (x \cos (x y) + 2) \frac{d y}{d x} = 0 .$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving the given exact differential equation

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Solve the exact differential equations in Exercises 63–66.ycos(xy)−3+(xcos(xy)+2)dydx=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

Mechanics Maths

Discrete Mathematics

Statistics

Applied Mathematics

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve the exact differential equations in Exercises 63–66. $y \cos (x y) - 3 + (x \cos (x y) + 2) \frac{d y}{d x} = 0 .$