1. Determine whether the statement is true or false. If it is true, explain why. If it false, explain why or give an example that disproves the statement. a. All solutions of the differential equation y'= -1- y are decreasing functions. b. The equation y' = x +y is separable. c. The equation exy' = y is linear.
1. Determine whether the statement is true or false. If it is true, explain why. If it false, explain why or give an example that disproves the statement. a. All solutions of the differential equation y'= -1- y are decreasing functions. b. The equation y' = x +y is separable. c. The equation exy' = y is linear.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Determine whether the statement is true or false. If it is true, explain why. If it false, explain why or give an
example that disproves the statement.
All solutions of the differential equation y' = -1- y4 are decreasing functions.
b. The equation y' = x + y is separable.
c. The equation e*y' = y is linear.
d. If y is the solution of the initial-value problem:
а.
dy
= 2y (1 -) y(0) = 1
dx
then lim y = 5.
t-00
2. Solve the differential equation:
a. y' = xe- sinx
- y cos x
b. 2yey' = 2x + 3Vx
3. Solve the initial-value problem:
+ 2tr = r, r(0) = 5
b. ху' — у %3D х Iп у, У(1) %3D 2
а.
4. Find the orthogonal trajectories of the family of curves: y = ke*
5. Solve the unknown function = ay (1 – by)
dy
dx
6. Given y(0) = ½ , solve = 3x²y².
dy
%3D
dx
7. Derive the orthogonal trajectories of the family of hyperbolas xy = c.
8. Determine the curve that passes through (5, - 1) such that every normal line to the curve passes through the
point (1, 2).
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