Consider the IVP y'' + 3y' + 3y = (1 − u(t − 4)) with y'(0) = 0 and y(0) = 0. Solve the differential equation, and if possible, provide a graph
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the integrating factor method. (b) What is the largest interval on which its solution is guaranteed to uniquely exist? (c) The equation is also separable. Solve it again as a separable equation. Find the particular solution of this IVP. Does your answer agree with that of part (a)? 5 Find the general solution of the differential equation. Do not solve explicitly for y. 6,/Solve explicitly...
Question 1 Given the following first order IVP: -y=e", y(0) = 0 1. Determine if the equation is linear, separable and/or Bernoulli (0.5 pt] 2. Solve the IVP using one of applicable methods studied (integrating factor, separation of variable and/or substitution of variables) (2 pt] 3. Now solve it again using the Laplace Transform [2 pt] 4. Which method did you find easier and why? [0.5 pt]
Question 1 Given the following first order IVP: -y=e", y(0) = 0 1. Determine if the equation is linear, separable and/or Bernoulli (0.5 pt] 2. Solve the IVP using one of applicable methods studied (integrating factor, separation of variable and/or substitution of variables) (2 pt] 3. Now solve it again using the Laplace Transform [2 pt] 4. Which method did you find easier and why? [0.5 pt]
Solve the IVP using laplace transformation y”+3y=(t-2)u(t-1) y(0)=-1 y’(0)=2 Solve the IVP usiag laplace transformahbn 3y (t-2) u (t-1) (0) 2 yo)-1 Solve the IVP usiag laplace transformahbn 3y (t-2) u (t-1) (0) 2 yo)-1
7: Problem 7 Previous Problem List Next (1 point) Solve the differential equation y" + 2/-3y-1+ 2 3 (1), y(0)-2, y (0)--2 using Laplace transforms. The solution is y(t)- and for 0 < t <3 for t > 3 7: Problem 7 Previous Problem List Next (1 point) Solve the differential equation y" + 2/-3y-1+ 2 3 (1), y(0)-2, y (0)--2 using Laplace transforms. The solution is y(t)- and for 0
7. Consider the first order differential equation 2y + 3y = 0. (a) Find the general solution to the first order differential equation using either separation of variables or an integrating factor. (b) Write out the auxiliary equation for the differential equation and use the methods of Section 4.2/4.3 to find the general solution. (c) Find the solution to the initial value problem 2y + 3y = 0, y(0) = 4.
differential equation Convert the IVP into an IVP for a system in normal ( canonical) form: y(+y(O-340=t; x0- 3; y(o = -6 a) b.) Given F(s)= - . Find (f f)( dv= J Solve the integral equation: c) Solve the IVP using Laplace transforms: d.) ty+y-y-O,XO) = 0; y(0) =1 Convert the IVP into an IVP for a system in normal ( canonical) form: y(+y(O-340=t; x0- 3; y(o = -6 a) b.) Given F(s)= - . Find (f f)( dv=...
pls do all questions. thanx 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)...
(1 point) Solve the differential equation -1, y (0)2 y-4y -5t263 (t) y(0) using Laplace transforms. for 0 t3 The solution is y(t and y(t) for t> (1 point) Solve the differential equation -1, y (0)2 y-4y -5t263 (t) y(0) using Laplace transforms. for 0 t3 The solution is y(t and y(t) for t>