8. Consider the DE: y' =y-2 e Label the isoclines below by the corresponding values a) of m: 0, 1, t2 b) Find the region where the solutions are decreasing. Draw the direction field c) d) Sketch two solutions passing respectively through the points (0, 0) and (2, 2) (15 pts) 4 3 2 -2 -3
8. Consider the DE: y' =y-2 e Label the isoclines below by the corresponding values a) of m: 0, 1, t2 b) Find the...
The isoclines of the first order differential
equation
are the family of parallel lines with slope 2. Use the drop-down
menus to answer each of the following questions.
Question 5 2.5 / 10 pts The isoclines of the first order differential equation dy dar 2x – Y are the family of parallel lines with slope 2. Use the drop-down menus to answer each of the following questions. (1) What is the slope of all solution curves as they pass through...
DO HAND CALCULATIONS. SHOW ALL STEPS
1. Slope Fields For the given differential equations sketch the slope fields and some of the isoclines. Then sketch some of the solution curves and verify your answer by solving the differential equation. a) dy-2 dx y
1. Slope Fields For the given differential equations sketch the slope fields and some of the isoclines. Then sketch some of the solution curves and verify your answer by solving the differential equation. a) dy-2 dx y
Determine state-space model of the following ODE 10 -2] L2 ri y(t) = [1 1] T2 10 21 T1 1」 [22 T1 10 -2] Lx2 T2 y(t)= [1 ollzi
for all points on the graph of y = 2cos x+5 where the slope of the 6. Find the values of x in OSx< tangent line is -1. (10 pt) be
If you were to plot the coulomb’s law formula on a graph , where the slope is equal to kq1q2. Y axis is F and x-axis is 1/r. The equation for the graph is a linear equation where m=slope and b=intercept. What is the meaning/value of this intercept. Example Graph : F vs 1/r y= mx + b y=(k*2.6x10^-9)x + 2.3x10^-6 Where m=kq1q2 , what would b represent ?
Consider the ODE dy/dt = -y(1-(y/T))(1-(y/K)) where 0 < T < K. (a) Draw a phase line and determine the stability of each equilibrium point. (b) Draw a graph in the yt-plane showing several solutions and their long term behavior. (Remark: Solving this ODE isn’t necessary!)
8) Find the points (x,y) on the curve given by x = 1+t2 and y=t-t3 where the tangent line is horizontal. Graph the curve and locate these points. Provide scales on both axes. Suggestion: On Desmos, let-2 st s 2 to see the full curve and to estimate where these points are. Points
Consider an autonomous ODE y = f(y) where f(y) = y2 - 1 A. (1 pt) Draw the graph of function f(y) in the y,y plane and specify the points y where f(y) is singular (that is, f(y) takes an infinite value). B. (1 pt) Finf the equilibrium solution and determine its type: stable, un- stable or semi-stable. Indicate on which side it attracts/repels nearby solutions. C. (2 pt) By separating y and t, specify the general solution y=yt,C) t+C...
3. A ODE is called autonomous if it contains no independent variables. That is y f (x, y) is actually just g(y). Draw a ODE slope field for the following autonomous f2y722y 3 + Sketch a solution that goes through y(0) = -1 and also sketch the solution that goes through y(0) 0.
3. A ODE is called autonomous if it contains no independent variables. That is y f (x, y) is actually just g(y). Draw a ODE slope field...