(1 point) It can be helpful to classify a differential equation, so that we can predict...
Question 2 (1 point) Saved Classify the differential equation by order and linearity. dy co3y sin (2t COS Nonlinear, second order differential equation Linear, first order differential equation Nonlinear, first order differential equation Linear, second order differential equation
1. Classify each ordinary differential equation as to order (1st, 2nd, etc) and type (linear/nonlinear). a) y' + 2y + 3y = 0 b) y" + 2yy + 3y = 0 c) y" + 2y' + 3xy - 4e" y sin 3
problem 34 Equations with the Independent Variable Missing. If a second order differential equation has the form y"f(y, y), then the independent variable t does not appear explicitly, but only through the dependent variable y. If we let y', then we obtain dv/dt-f(y, v). Since the right side of this equation depends on y and v, rather than on and v, this equation is not of the form of the first order equations discussed in Chapter 2. However, if we...
i. 1. Answer each of the following For each of the following differential equations, state the order of the equation and state whether it is linear or nonlinear. If the differential equation is linear, state whether it is homogeneous or nonhomogeneous dy + + xy = sin x dx 2 a. dx2 b. x6y(5) – x2y'" – (cos x )y – ex = 0 ii. Find the value(s) of m so that the function y = xº, x 0 is...
(1 point) General Solution of a First Order Linear Differential Equation A first order linear differential equation is one that can be put in the form dy + P(2)y= Q(1) dz where P and Q are continuous functions on a given interval. This form is called the standard form and is readily solved by multiplying both sides of the equation by an integrating factor, I(2) = el P(z) da In this problem, we want to find the general solution of...
mat lab only Osts 10 Problem 3 Numerically integrate the 2nd order linear differential equation on the interval +5 + 4y - 0 v0-0 0-6 y(t) - 2e" - 2e-41 and compare it to the solution a) Plot the numerical solution and the true solution for y(t) (20 pts) b) Plot the numerical solution and the true solution for dy/dt (10 pts)
4. Consider this second order linear differential equation 2d¢y _5r° dy +8y 0 dr dr2 = r solve the DE. Show that there are (a) Find numbers m such that y(x) two such m, and we call them m,m2 exactly (b) Show that y(x) = cir"1 + czr*m# also solves the DE, where ci,c2 are arbitrary constants (c) Can you find ,2 so that y(x) solves the following initial value problem? y(1) 0 /(1)2 (d) Can you find c,c2 so...
(1 point) a. Consider the differential equation: d2y 0.16y-0 dt2 with initial conditions dt (0)-3 y(0)--1 and Find the solution to this initial value problem b. Assume the same second order differential equation as Part a. However, consider it is subject to the following boundary conditions: y(0)-2 and y(3)-7 Find the solution to this boundary value problem. If there is no solution, then write NO SOLUTION. If there are infinitely many solutions, then use C as your arbitrary constant (e.g....
using matlab thank you 3 MARKS QUESTION 3 Background The van der Pol equation is a 2nd-order ODE that describes self-sustaining oscillations in which energy is withdrawn from large oscillations and fed into the small oscillations. This equation typically models electronic circuits containing vacuum tubes. The van der Pol equation is: dt2 dt where y represents the position coordinate, t is time, and u is a damping coefficient The 2nd-order ODE can be solved as a set of 1st-order ODEs,...
(1 point) We know that y(x) 72 is a solution to the differential equation Dy - Dy - 98y = 0 for 2 € (-00,00). Use the method of reduction of order to find the second solution to Dy - Dy - 98y = 0 for x € (-0,00) (a) After you reduce the second order equation by making the substitution w = ' you get a first order equation of the form f(x,x) = Note: Make sure you use...