1 Consider the IVP: y' = (2y+t)? y(3) = 2 2 The Taylor method of order...
Consider the second-order IVP: t2y''+ty'-4y=-3t , t in [1,3] and y(1)=4 and y'(1)=3 Solve using Modified Euler's Method with h=1, by first transforming into a first-order IVP and solving.
[7] 1. Consider the initial value problem (IVP) y′(t) = −y(t), y(0) = 1 The solution to this IVP is y(t) = e−t [1] i) Implement Euler’s method and generate an approximate solution of this IVP over the interval [0,2], using stepsize h = 0.1. (The Google sheet posted on LEARN is set up to carry out precisely this task.) Report the resulting approximation of the value y(2). [1] ii) Repeat part (ii), but use stepsize h = 0.05. Describe...
pls do all questions.
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1. [5 Consider the IVP rty(t) + 2 sin(t)y(t) = tan(t) y(5)=2 Does a unique solution of the IVP exist? Do not solve the IVP but fully justify you answer. What is the IOE? 2. 4 Consider the ODE Using undetermined coefficients, what is an approprite guess for the coefficient (s) in yp but fully justify you answer. ? Do not solve for 3. [10] Solve the IVP. Use any approach you like y(x) 6y'(x)...
Question 2 Given the following second order IVP: y" – 2y' + y = e*, y(0) = 0, y'(0) = 1. 1. Solve it using the undetermined coefficients method. [2 pt] 2. Solve it again using the Laplace Transform. (2.5 pt] 3. Which method did you find easier and why? [0.5 pt]
Question 2 2 pts Consider the solution to the IVP y - ry=2; y(0) = 2 Find y' (0) Question 3 2 pts Consider the solution to the IVP y - ry=r; y(0) = 2 Find y" (0) Question 4 4 pts Consider the solution to the IVP w"-() = 0; y(0) = 1; 7 (0) = 2 Find the coefficient of in its Taylor expansion centered ato.
) For the IVP y+2y-2-e(0)- Use Euler's Method with a step size of h 5 to find approximate values of the solution at t-1 Compare them to the exact values of the solution at these points.
Problem 2: [Also challenging] Find the solution of the following IVP: y' +2y = g(t), with y(0) = 3 where g(t) = - 0<t<1: g(t) = te-2 > 1.
Problem 1
1. Consider the third order equation 2 t²y' - 2y" -3t" Q. Write the equation above as an equivalent First order differential equations. Use x =Y , X2=4' and x3=y". system of b. express your system of equations in matrix vector form: = Alt) R + g(+)
- 2y²,y(0) =0. 1+x² 4) Consider the IVP y'= х a) Verify that y= is the solution of this IVP. 1+x? b) Use Euler's method to numerically approximate the solution to this IVP over the interval [0,2] in x. Set the mesh width h=0.1. Calculate the true values of y atthe appropriate values of x as well as the error in your numerical approximation. Report your results in the table given. Report answers to four decimal places. Numerical Actual y...
5. Consider the following second order IVP y2y te - t, 0 t1 y(0)/(0) 0 = ( y(t). Transform the above IVP to system of first order (a) Let u(t)y(t) and u2(t) IVP of u and u2. (b) Find y(t) by solving the system with h 0.1 (c) Compare the results to the actual solution y(t) = %et - te 2e t - 2.
5. Consider the following second order IVP y2y te - t, 0 t1 y(0)/(0) 0 =...