(a) Draw a direction field for the given differential equation. (b) Based on an inspection of the...
Please help me with the following thermo question from the picture and below continuation (b) Based on an inspection of the direction field, describe how solutions behave for large t. All solutions seem to eventually have negative slopes, and hence decrease without bound.All solutions seem to eventually have positive slopes, and hence increase without bound. The solutions appear to be oscillatory.If y(0) > 0, solutions appear to eventually have positive slopes, and hence increase without bound. If y(0) ≤ 0,...
Draw a direction field for the given differential equation and state whether you think that the solutions for t >0 are converging or diverging. yy(3 ty) - Converge. Diverge Converge for y 20,diverge for y< 0 Converge for y<U, diverge for y 2 0 Draw a direction field for the given differential equation and state whether you think that the solutions for t >0 are converging or diverging. yy(3 ty) - Converge. Diverge Converge for y 20,diverge for y
Find the general solution of the given differential equation, and use it to determine how solutions behave as t → 0. y + 7y = t+e-5t QC. 0 Solutions converge to the function y =
Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y at t -> oo. If this behavior depends on the initial value of y at t 0, describe this dependency. (b) y'-2t-1-y.
Consider the differential equation dy -0.5y (y – 4) dt Question 1 Why is the given differential equation considered autonomous?" The derivative of the unknown function(y) is described only in terms of y, not t. The derivative of the unknown function (y) is a first derivative, not a second derivative. The derivative of the unknown function(y) is described only with linear factors such as -0.5y and (y-4), not curves such as sin(y) or 1/y. Question 2 As a step toward...
First, verify that y(x) satisfies the given differential equation. Then, determine a value of the constant C so that y(x) satisfies the given initial condition. Use a computer or graphing calculator to sketch several typical solutions of the given differential equation, and highlight the one that satisfies the given initial condition. y' =y+3; y(x) = CeX-3; y(0) = 8 What step should you take to verify that the function is a solution to the given differential equation? O A. Differentiate...
Differential equation class. Please show steps to the solutions. Section 3.3 Exercises To Solutions For all exercises in this section you will be working with the equation dt for various values of m, β and k. but always with f(t)-0. 1. (a) Solve the initial value problem consisting of Equation (1) withm-5, B- and k 80, and initial conditions y(02, y(0)-6. Give your answer in the form y Cesin(wt and all numbers in decimal form, rounded to the nearest tenth....
plz print ur answer Question2 Consider the differential equation We saw in class that one solution is the Bessel function (-1)" ( 2n+2 2+n)! 2) n=0 (a) Suppose we have a solution to this ODE in the form y = Σ。:0cmFn+r where 0. By considering the first term of this series show that r must satisfy r2-4=0(and hence that r = 2 or r=-2). (b) Show that any solution of the form y-must satisfy co c) From the theory about...
write MATLAB scripts to solve differential equations. Computing 1: ELE1053 Project 3E:Solving Differential Equations Project Principle Objective: Write MATLAB scripts to solve differential equations. Implementation: MatLab is an ideal environment for solving differential equations. Differential equations are a vital tool used by engineers to model, study and make predictions about the behavior of complex systems. It not only allows you to solve complex equations and systems of equations it also allows you to easily present the solutions in graphical form....
Given a second order linear homogeneous differential equation a2(x)” + a (x2y + a)(x2y = 0 we know that a fundamental set for this ODE consists of a pair linearly independent solutions yı, y. But there are times when only one function, call it yi, is available and we would like to find a second linearly independent solution. We can find y2 using the method of reduction of order. First, under the necessary assumption the az(x) + 0 we rewrite...