![(d) [5 pts] Draw the phase line, and sketch a graph of each of the qualitatively dif- ferent solution curves in the ty-plane.](http://img.homeworklib.com/questions/a5726ff0-9907-11eb-ab1d-75d838b831c0.png?x-oss-process=image/resize,w_560)
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7. Answer the questions below for the following initial value problem: y (t) = sin y,...
Using Differential Equations. 6. For y, = y3 _ y, y(0) = 30, -00 <30 <...
Using Differential
Equations.
6. For y, = y3 _ y, y(0) = 30, -00 <30 < 00, draw the graph of (y) = y3-y versus y, determine the equilibrium solutions (critical points) and classify each one as unstable or asymptotically stable. Draw the phase line, and sketch several representative integral curves (graphs of solutions) in the (t, y) plane. Hint: None of this requires explicit formulas for solutions y = φ(t) of the initial value problem.]
6. (2 pts) Consider the following initial value problem: y' = (t + y)?y2 + sin(yº)...
6. (2 pts) Consider the following initial value problem: y' = (t + y)?y2 + sin(yº) + yety, y(0) = 0. This initial value problem satisfies the existence and uniqueness theorem criteria using interval (-0, 0) for both thet and y variables, and hence has a unique solutoin. Find this unique solution. Hint: None of the techniques we've learned for explicitly solving will work. Instead, try plugging the initial condition into the differential equation and think about what that tells...
Problem 5. (20 pts) Let f(y) be the real function f: R R depicted in Figurei,...
Problem 5. (20 pts) Let f(y) be the real function f: R R depicted in Figurei, and consider the autonomous differential equation y(t) = f(y(t)). fly) у FIGURE 1. The function f(y) for Problem 4. (a) How many constant solutions does the above differential equation have ? (b) Study whether the behaviour of each of the constant solutions of the differential equation y(t) = f(y(t)) is stable, unstable or semistable. (c) Discuss the long-term behaviour of all solutions y(t) to...
Find y(t) solution of the initial value problem 2 y2 +bt2 y'= y(1) = 1, t>0,...
Find y(t) solution of the initial value problem 2 y2 +bt2 y'= y(1) = 1, t>0, ty
Consider the following initial value problem dy dt = (1 – t)y + sin y with...
Consider the following initial value problem dy dt = (1 – t)y + sin y with y(-1) = 0.5 We want to find y(2) with an absolute error below 10-8.
Solve the following initial value problem using ode45 and ode15s: y",(t) _ Зу"(t) + ty(t) _ sin2(...
Solve the following initial value problem using ode45 and ode15s: y",(t) _ Зу"(t) + ty(t) _ sin2(t)-7, o s t Plot the solution for varying tolerances. Why do you believe your solution is cor- 2. 1, y(0)-0, y,(0) 1, y"(0)-0. rect?
Solve the following initial value problem using ode45 and ode15s: y",(t) _ Зу"(t) + ty(t) _ sin2(t)-7, o s t Plot the solution for varying tolerances. Why do you believe your solution is cor- 2. 1, y(0)-0, y,(0) 1,...
Use the Laplace transform to solve the given initial-value problem. y'' + y = 2 sin( 2 t), y(0) = 11, y'(0) = 0 y(t) =
Use the Laplace transform to solve the given initial-value problem.y'' + y = 2 sin(2t), y(0) = 11, y'(0) = 0y(t) =
Use the Laplace transform to solve the given initial-value problem. y'' + y = 2 sin( 2 t), y(0) = 11, y'(0) = 0 y(t) =
Use the Laplace transform to solve the given initial-value problem.y'' + y = 2 sin(2t), y(0) = 11, y'(0) = 0y(t) =
Answer is B If y(t) is the solution of the initial value problem then y(t) =?...
Answer is B
If y(t) is the solution of the initial value problem then y(t) =? A. u5(t)e2f sin t B. us(t)e2t+10 sin(t - 5) C. s(t2t-5 sin(2t - 10) 2 D. us(t)e2-5 sin(t - 5) E. ušt)e-2t+10 cos(t-5
Use the Laplace transform to solve the given initial-value problem. y" + y = V2 sin...
Use the Laplace transform to solve the given initial-value problem. y" + y = V2 sin it, y(0) = 13, y'(0) = 0 y(t) =
Using Differential
Equations.
6. For y, = y3 _ y, y(0) = 30, -00 <30 < 00, draw the graph of (y) = y3-y versus y, determine the equilibrium solutions (critical points) and classify each one as unstable or asymptotically stable. Draw the phase line, and sketch several representative integral curves (graphs of solutions) in the (t, y) plane. Hint: None of this requires explicit formulas for solutions y = φ(t) of the initial value problem.]
6. (2 pts) Consider the following initial value problem: y' = (t + y)?y2 + sin(yº) + yety, y(0) = 0. This initial value problem satisfies the existence and uniqueness theorem criteria using interval (-0, 0) for both thet and y variables, and hence has a unique solutoin. Find this unique solution. Hint: None of the techniques we've learned for explicitly solving will work. Instead, try plugging the initial condition into the differential equation and think about what that tells...
Problem 5. (20 pts) Let f(y) be the real function f: R R depicted in Figurei, and consider the autonomous differential equation y(t) = f(y(t)). fly) у FIGURE 1. The function f(y) for Problem 4. (a) How many constant solutions does the above differential equation have ? (b) Study whether the behaviour of each of the constant solutions of the differential equation y(t) = f(y(t)) is stable, unstable or semistable. (c) Discuss the long-term behaviour of all solutions y(t) to...
Find y(t) solution of the initial value problem 2 y2 +bt2 y'= y(1) = 1, t>0, ty
Consider the following initial value problem dy dt = (1 – t)y + sin y with y(-1) = 0.5 We want to find y(2) with an absolute error below 10-8.
Solve the following initial value problem using ode45 and ode15s: y",(t) _ Зу"(t) + ty(t) _ sin2(t)-7, o s t Plot the solution for varying tolerances. Why do you believe your solution is cor- 2. 1, y(0)-0, y,(0) 1, y"(0)-0. rect?
Solve the following initial value problem using ode45 and ode15s: y",(t) _ Зу"(t) + ty(t) _ sin2(t)-7, o s t Plot the solution for varying tolerances. Why do you believe your solution is cor- 2. 1, y(0)-0, y,(0) 1,...
Answer is B
If y(t) is the solution of the initial value problem then y(t) =? A. u5(t)e2f sin t B. us(t)e2t+10 sin(t - 5) C. s(t2t-5 sin(2t - 10) 2 D. us(t)e2-5 sin(t - 5) E. ušt)e-2t+10 cos(t-5
Use the Laplace transform to solve the given initial-value problem. y" + y = V2 sin it, y(0) = 13, y'(0) = 0 y(t) =
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