(1) Give the general solutions of the following DE and solve the IVP. (a) 42y" 3zy 3y 82/3, given...
solve the given DE or IVP (Initial-Value Problems) In Problems 2-5, solve the given DE or IVP (Initial-Value Problems) 3. y sin2 (4x - 4y +3)
In Problems 1-3, solve the given DE or IVP (Initial-Value Problem). [First, you need to determine what type of DE it is.) 1. (2xy + cos y) dx + (x2 – 2 siny – 2y) dy = 0. 2. + cos2 - 2ary dy dar y(y +sin x), y(0) = 1. 1+ y2 3. [2ry cos (x²y) - sin r) dx + r?cos (r?y) dy = 0. 4. Determine the values of the constants r and s such that (x,y)...
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
solution for all 4 please In Problems 1-3, solve the given DE or IVP (Initial-Value Problem). [First, you need to determine what type of DE it is. 1. (2xy + cos y) dx + (x2 – x sin y – 2y) dy = 0. 1 dy 2. + cos2 - 2.cy y(y + sin x), y(0) = 1. + y2 dc 3. [2xy cos (2²y) – sin x) dx + x2 cos (x²y) dy = 0. (1+y! x" y® is...
(b) (30 points) Solve the following IVP given that yı (x) = x and y2 (x) = x3 are solutions to the corresponding homogeneous differential equation. Be sure to fully evaluate any integrals that arise. (You will have to use polynomial long division.) " - 3xy' + 3y = y(1) = 0, y(1) = 0 1+2
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...
solve the given de or ivp 3. [2xy cos (x²y) - sin x) dx + rcos (2²y) dy = 0.
. Consider the IVP: y + 3y = e 3t, y(0) = 1, y(0) = 0 - Solve the IVP using the guess and test method. .Solve the IVP using the general formula for integrating factors. - Solve the IVP using Laplace Transforms. . Verify that your solution satisfies the differential equation (you should get the same solution using Il three methods, so you only need to test it once).
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
1. For each DE, clearly identify the characteristic equation, then solve to find the general solution: a) y" +2 y' - 3y = 0 (3 pts) b) y) - 4y" +4y' = 0 (4 pts)