Find the particular solution of the differential equation dy/dx=y−5/x−8 using the given boundary condition: y=7 when x=9. (Use symbolic notation and fractions where needed.)

General Formulas and Concepts:

Symbols

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Functions

Point-Slope Form: y - y₁ = m(x - x₁)

Slope-Intercept Form: y = mx + b

Algebra II

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

Slope Fields

Solving Differentials - Integrals

Integration Constant C

U-Substitution

ln Integration:

Step-by-step explanation:

*Note:

When solving differential equations in slope fields, disregard the integration constant C for variable y.

Step 1: Define

x = 9, y = 7

Step 2: Rewrite Differential

Rewrite Leibniz Notation using Separation of Variables.

Step 3: Integrate Pt. 1

Solving general form of differential using integration.

Step 4: Identify Variables

Set up u-substitution for right integral.

Integral w/ respect to y

u = y - 5

du = dy

Integral w/ respect to x

z = x - 8

dz = dx

Step 5: Integrate Pt. 2

General Form:

Step 6: Solve Particular Solution

Since both sides have absolute value, assume that the particular solution will be positive.

Substituting integration constant C into the general form:

Particular Solution (in Point-Slope Form):

Particular Solution (in Slope-Intercept Form):

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Differentials and Slope Fields

Book: College Calculus 10e

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles

5 pm

step-by-step explanation: