Question

Consider the differential equation y' = y2 − 9 . Let f(x, y) = y2 −...

Consider the differential equation
y' =

y2 − 9
.
Let
f(x, y) =

y2 − 9
.
Find the partial derivative of f.
df
dy
=
Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point
(x0, y0)
in the region.
A unique solution exits in the entire x y-plane.
A unique solution exists in the region −3 < y < 3.
A unique solution exits in the regions y < −3, −3 < y < 3, and y > 3.
A unique solution exists in the region y < −3 or y > 3.
A unique solution exits in the region consisting of all points in the x y-plane except (0, 3) and (0, −3).
Determine whether Theorem 1.2.1 guarantees that the differential equation possesses a unique solution through
(4, 3).
Yes
No
Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1) Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli...
1) Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation. x dy/dx +y= 1/y^2 2)Consider the following differential equation. (25 − y2)y' = x2 Let f(x, y) = x^2/ 25-y^2. Find the derivative of f. af//ay= Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0, y0) in the region. a) A unique solution exists in the region consisting...
determine if the xy-plane for which the given differential equation would have a unique solution whose...
determine if the xy-plane for which the given differential equation would have a unique solution whose graph passes through the point (x0,y0) in the region dy/dx=y^(2/3) x(dy/dx)=y
(a) verfiy that y=tan(x+c) ia a one parameter family of solutions of the differential equation y'=...
(a) verfiy that y=tan(x+c) ia a one parameter family of solutions of the differential equation y'= 1+x^2 (b)since f(x,y)= 1+y^2 and df/dy= 2y are continuous everywhere, the region R can be taken to be the entire xy-plane. Use the family of solutions in part A to find an explicit solution of the first order initial value problem y'= 1+y^2, y(0)=0. Even though x0=0 is in the interval (-2,2) explain why the solution is not defined on its interval (c)determine the...
Choose the correct answers If y1 and y2 are two solutions of a nonhomogeneous equation ayjj+...
Choose the correct answers If y1 and y2 are two solutions of a nonhomogeneous equation ayjj+ byj+ cy =f (x), then their difference is a solution of the equation ayjj+ byj+ cy = 0. If f (x) is continuous everywhere, then there exists a unique solution to the following initial value problem.                                   f (x)yj= y,   y(0) = 0 The differential equation yjj + t2yj − y = 3 is linear. There is a solution to the ODE yjj+3yj+y...
Topic: Calculus 3 / Differential Equation Q1) Let (x0, y0, z0) be a point on the...
Topic: Calculus 3 / Differential Equation Q1) Let (x0, y0, z0) be a point on the curve C described by the following equations F1(x,y,z)=c1 , F2(x,y,z)=c2 . Show that the vector [grad F1(x0, y0, z0)] X [grad F2(x0, y0, z0)] is tangent to C at (x0, y0, z0) Q2) (I've posted this question before but nobody answered, so please do) Find a vector tangent to the space circle x2 + y2 + z2 = 1 , x + y +...
Consider the differential equation y' = x − y + 1: (a) Verify that y =...
Consider the differential equation y' = x − y + 1: (a) Verify that y = x + e^(1−x) is a solution to the above differential equation satisfying y(1) = 2; (b) Is the solution through (1, 2) unique? Justify your answer in a few sentences; (c) Is this differential equation separable? Find the general solution of y' = x − y + 1.
Determine a region of the xy-plane for which the given differential equation would have a unique...
Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x_0, y_0) in the region. (1+y^3)y' = x^2
] Consider the autonomous differential equation y 0 = 10 + 3y − y 2 ....
] Consider the autonomous differential equation y 0 = 10 + 3y − y 2 . Sketch a graph of f(y) by hand and use it to draw a phase line. Classify each equilibrium point as either unstable or asymptotically stable. The equilibrium solutions divide the ty plane into regions. Sketch at least one solution trajectory in each region.
Assignment #3 Modeling and the Geometry of Systems 1. For this problem, we study the nonlinear...
Assignment #3 Modeling and the Geometry of Systems 1. For this problem, we study the nonlinear differential equation: dx dt = y dy dt = x − x^3 − y^3 a) Algebraically determine all of the equilibria to the differential equation . b) For a solution {x(t), y(t)} with {x(0), y(0)} = {x0, y0}, use your phase diagram to describe the long term behavior of the solution. 1. {x0, y0} = {1, 1} 2. {x0, y0} = {−1, −1} 3....
[3 marks] Consider the following statements about solutions  f (x) of the differential equation y′  = ...
[3 marks] Consider the following statements about solutions  f (x) of the differential equation y′  =  (xy − 7y − 9x + 63)esin x. (i) There is no k such that  f (x)  =  k is a solution. (ii) If  f (x)  <  9 then  f (x) is decreasing for x  <  0. (iii) If  f (x)  <  0, then  f (x) is increasing when x  >  7. Determine which of the above statements are True or False .
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT