



a)
Consider the following differential equation:
The objective is to reproduce the direction field and sketch a approximate solution curve through the point y(-2) = 1
The direction field of the differential equation is shown below:

The solution curve passing through point y(-2) = 1 is:

b)
The solution curve passing through point y(3) = 0 is:

c)
.The solution curve passing through point y(0) = 2 is:

d)
.The solution curve passing through point y(0) = 0 is:

Reproduce the given computer-generated direction field. Then sketch an approximate solution curve that passes through each...
Find a solution of x dy = y2 - y that passes through the indicated points. dx (a) (0, 1) y = (b) (0,0) y = (c) (60) ya (d) (6, 1) y =
5. Find a solution of a IVP consisting of the DE y-2 y=cie 3 6x+4, with solution 33 + coe-2x and initial conditions 1(1) 4, y'(1)-2 6. Given a direction field, sketch by hand an approximate solution curve that passes through a given initial condition (a) y(0) 0 (b) y(0) 2
5. Find a solution of a IVP consisting of the DE y-2 y=cie 3 6x+4, with solution 33 + coe-2x and initial conditions 1(1) 4, y'(1)-2
6. Given a...
The given figure represents the graph of f(y).
Sketch a direction field over an appropriate grid for
dy/dx = f(y).
solve please
8 Sketch the direction field of the differential equation dx dt Verify that x t-1 Ce is the solution of the equation. Sketch the solution curve for which x(0) 2, and that for which x(4) 0, and check that these are consistent with your direction field. MAPI R has tools for exam
8 Sketch the direction field of the differential equation dx dt Verify that x t-1 Ce is the solution of the equation. Sketch the solution curve...
Find the tangent equation to the given curve that passes through the point (18,9). Note that due to the t2 in the x equation and the t3 in the y equation, the equation in the parameter t has more than one solution. This means that there is a second tangent equation to the given curve that passes through a different point. x = 9t2 + 9 y = 6t3 + 3
Find the tangent equation to the given curve that passes through the point (4, 3). Note that due to the t2 in the x equation and the 3 in the y equation, the equation in the parameter t has more than one solution. This means that there is a second tangent equation to the given curve that passes through a different point. x = 3t2 + 1 y = 2t2 + 1
In each of Problems 1 through 4 draw a direction field for the given differential equations. Based on the direction field, determine the behavior of y as t → +∞. If this behavior depends on the initial value of y at t = 0, describe this dependency. 1. y ' = 3 + 2y 2. y ' = 3 − 2y 3. y ' = −y(5 − y) 4. y ' = y(y − 2)2
Find the tangent equation to the given curve that passes through the point (4, 3). Note that due to the t2 in the x equation and the 3 in the y equation, the equation in the parameter t has more than one solution. This means that there is a second tangent equation to the given curve that passes through a different point. x = 3t2+1 y = 2t3 + 1 y = (tangent at smaller t) y = (tangent at larger t)
Consider the differential equation dy/dx = (y-1)/x. (a) On the axes provided, sketch a slope field for the given differential equation at the nine points indicated. (b) Let y = f (x) be the particular solution to the given differential equation with the initial condition f (3) = 2. Write an equation for the line tangent to the graph of y= f (x) at x = 3. Use the equation to approximate the value of f (3.3). (c) Find the particular solution y...
help d, e h j k
● Sketch slope fields and approximate solution curves for the given DEs and initial condi- tions: y' = t + y, y(-1)= 2, y(0)--1. y, = t-y, y(-1) = 2, y(0) =-1. yt , y(-1) 0, y(0) 1 t,y(0)-0, (0) -0.6, (0) 0.8. nothev
● Sketch slope fields and approximate solution curves for the given DEs and initial condi- tions: y' = t + y, y(-1)= 2, y(0)--1. y, = t-y, y(-1) = 2,...