Answer all Please! Thanks 1. Confirming Solutions to Differential Equations: Verify that each function does in fact solve the given differential equation. If there are parameters in the function (A....
Please show solutions. Answer: 1. Find a general solution to the following differential equations: (a) y" + y = 0 (b) y" – 2y' + 264 = 0 (c) 4x²y" – 3y = 0 (d) y" + 4y = 9 sin(t). (e) y" – 6y' + 9y = 6e3x 1. (a) y = ci + c2e- (b) y = cle' cos(5t) + czet sin(5t) (c) y = cit-1/2 + c2t3/2 (d) y = ci cos(2t) + c2 sin(2t) + 3...
verify that the given function is a solution to the given differential equation (c1 andc2 arbitrary constants), and state the maximum interval over which the solution is valid. 8. y(x) = cj cos 2x + c2 sin 2x, y + 4y = 0.
1. Solve the following Differential Equations. 2. Use the variation of parameters method to find the general solution to the given differential equation. 3. a) y" - y’ – 2y = 5e2x b) y" +16 y = 4 cos x c) y" – 4y'+3y=9x² +4, y(0) =6, y'(0)=8 y" + y = tan?(x) Determine the general solution to the system x' = Ax for the given matrix A. -1 2 А 2 2
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...
Differential equations for engineering I need the final answer please Verify by substitution that the given functions form a basis. Solve the given initial value problem y" + 18y' +90y = 0, -** cos (3x), e-% sin (3x), y(0) = 1, y (0) = -9 Enclose arguments of functions in parentheses. For example, sin (29x). Use an asterisk. * to indicate multiplication. For example, 2* f (x).a*** (x+b) * (c**+ d), b * tan(a *) or e(*) * b. Q
please answer questions 1-10. need to verify that my answers are correct. Find the value of the constant C so that the solution satisfies the initial value. 1. y' = 2x and y(3)= 7. y = x2 + C 2. y' = 3x2 - 5 and y(1) = 2. y = x3 - 5x + C 3. y' = 3y and y(0) = 5. y = Ce3x. 4. y'= -2y and y(0) = 3. Y = Ce-2x. Solve the differential...
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) Match each differential equation to a function which is a solution. FUNCTIONS A. y = 3x + x2, B.y= e 4x, C.y=sin(x), D.y=x2, E. y = 3 exp(62), DIFFERENTIAL EQUATIONS 1. y' +y=0 2. 2x²y" + 3xy' = y 3. y' = 6y 4. y" + 10y' + 24y = 0
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....
Differential Equation Please answer both of the questions below Thanks! Solve the given initial value problem. y'' + 36y = 0; y(0) = 3, y'(O) = 5 x(t) = Find a general solution to the differential equation using the method of variation of parameters. y'' + 2y' +y=2e -t The general solution is y(t) = .