(1 point) Find the general solution, y(t), which solves the problem below, by the method of...
(1 point) Find the general solution, y(t), which solves the problem below, by the method of integrating factors. 6t+y=t", t> 0 dt Put the problem in standard form. Then find the integrating factor, y(t) = and finally find y(t) = (use C as the unkown constant.)
(1 point) Solve the initial value problem 13(t+1) 94 – 9y = 36t, fort > -1 with y(0) = 10. Put the problem in standard form. Then find the integrating factor, p(t) = and finally find y(t) = 1
(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...
Previous Problem Problem List Next Problem (1 point) Let's find the general solution to z2y"-5zy, + 8y-(2-P) using reduction o of order (1) First find a non-trivial solution to the complementary equation z' smaller power m. 5zy' +8y0 of the form z. There are two possibilities, pe (2) Now set u = tizm and determine a first order equation (in standard form) that ,' t' must satisfy (3) Solve this for z using cl as the arbitrary constant 4) Solve...
dy Find the general solution of the differential equation: dt 2ty + 4e -ť. What is the integrating factor? u(t) = Use lower case c for the constant in answer below. y(t) =
(1 point) A first order linear equation in the form y' + p(x)y = f(x) can be solved by finding an integrating factor u(x) = expl (1) Given the equation xy' + (1 +4x) y = 10xe 4* find y(x) = (2) Then find an explicit general solution with arbitrary constant C. y = (3) Then solve the initial value problem with y(1) = e-4 y =
2. Consider the equation aty' +by = tº,y(1) =d where a,b,c and d are constants. For this question you will solve the problem via the Integrating Factor method. Do so following the steps below. A. Put the equation in standard form B. Find the integrating factor C. Multiply the equation by the integrating factor D. Assume +c=2 and integrate to solve the equation. E. Find the constant of the solution in part D in terms of a, b,c,d) using the...
(1 point) A first order linear equation in the form y p(x)yf(x) can be solved by finding an integrating factor x)expp(x) dx (1) Given the equation y' +2y-8x find u(x) - (2) Then find an explicit general solution with arbitrary constant C. (3) Then solve the initial value problem with y(0) 2 y-
Using the integrating factor method, find the general solution of the differential equation: y + 2 y = 4 x>0. y = x + 2 5 ºr - Syno 04 - 1 - /
Problem 22. Find the general solution to the Cauchy problem in implicit form (t sin(y)y' = 1 +cos(y) Solution. - - I cos(y(t)) = c.