For two different values of r, the function y(t)= t' satisfies the differential equation ty" –...
Problem 1. (1 point) A function y(t) satisfies the differential equation ay = – 44 – 6y2 + 7y?. (a) What are the constant solutions of this equation? Separate your answers by commas. (b) For what values of y is y increasing? <y< Note: You can earn partial credit on this problem.
Consider the differential equation: xạy" + 15xy' + 48y = 0. Find all values of r such that y=r" satisfies the differential equation for x > 0. If there is more than one correct answer, enter your answers as a comma separated list. r=
Find the function y = y(2) (for x > 0) which satisfies the separable differential equation dy 6 + 14.2 dic 12 2 0 with the initial condition y(1) = 3. y=
Problem List Previous Problem (15 points) Find the function y(t) that satisfies the differential equation dy 2ty = -15te dt and the condition y(0) = -5. M) =
3. Consider the differential equation ty" - (t+1)y + y = t?e?', t>0. (a) Find a value ofr for which y = et is a solution to the corresponding homogeneous differential equation. (b) Use Reduction of Order to find a second, linearly independent, solution to the correspond- ing homogeneous differential equation. (c) Use Variation of Parameters to find a particular solution to the nonhomogeneous differ- ential equation and then give the general solution to the differential equation.
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...
(1 point) A function X(t) satisfies the differential equation di = (x − 2)(x – 5)²(x – 7)(x – 9)?. Compute the following limits. You can use words like “Infinity” and “DNE” if you need to. If x(0) = 3.5, then lim x(t) = DNE help (numbers) too If æ(0) = 6, then lim x(t) = DNE help (numbers) t- o If x(0) = 8, then lim x(t) = DNE help (numbers) to
Consider the function Let where f(t) is differentiable for all t ∈ R. Show that z satisfies the partial differential equation (x2 − y2 ) ∂z/∂x + xy ∂z/∂y = xyz for all (x, y) ∈ R2 \ { (t, 0)|t ∈ R }.
Verify by substitution that the given function is a solution of the given differential equation. Note that any primes denote derivatives with respect to x. y' = 4x3y = x + 6 What step should you take to verify that the function is a solution to the given differential equation? O O O O A. Substitute the given function into the differential equation, B . Integrate the function and substitute into the differential equation C . Determine the first and...
Q1 (10 points) Consider the differential equation ty" _ y = 0. a) is this differential equation linear? What is its order? Is it homogeneous? b) Try a solution of the form y=x". Is this a solution for some r? If so, find all such r. c) Based on your answer to a) about linearity and b) about what y=x" are solutions, make an educated guess a the general solution looks like. Try that guess and check that it works....