2) (10) Find the integrating factor and solve the initial value problem -2xy + y(1) Find...
2. Integrating factor Solve the given initial value problem. a) (1 + x*)y' + 2xy = f(x), y(0) = 0 f(x) = {-x, x<0 x, x20
(1 point) In this exercise you will solve the initial value problem 1 +x2' (1) Let Ci and C2 be arbitrary constants. The general solution to the related homogeneous differential equation " - 4y+4y 0 is the function C2 NOTE: The order in which you enter the answers is important, that is, CJU) + Gg(x)ヂGg(x) + CN 2) The particular solution yo(x) to the differential equation y" +4ys of the form yo) -yi) u)x) and (x) = 2x (3) The...
(1 point) In this exercise you will solve the initial value problem e-9 y" – 184' +81y = 4472; y(0) = -3, v'(0) = -2. (1) Let C and Cybe arbitrary constants. The general solution to the related homogeneous differential equation y" – 18y' +81y = 0 is the function yh() = C1 yı() + C2 y2() = C1 +C2 NOTE: The order in which you enter the answers is important; that is, Cif(T) + C29(2) #C19() +C2f(). is of...
PROBLEM Solve the initial value problem (we discuss how to do this, but did not yet do this in class) x¨ + ω2x = sin(ωt), x(0) = x˙(0) = 0 First step: find a solution to the non-homogeneous equation. PROBLEM Find a solution of non-homogeneous equation x¨ + ω2x = cos2(ωt) Hint: use previous lecture material and homework to represent cosine-squired as a sum of trigonometric functions.
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
1. Solve the following homogeneous differential equation. ty' = 1. cos (6) + y 2. Solve the following Bernoulli differential equation 3. Solve the following initial value problem. (Hint: transform the equation to a separable equation through a substitution) y-(x + y + 1)? (0) - V3 - 1 4. Let T represent the temperature (in °F) of an object in a room whose temperature is kept at a constant 60°. If the object cools from 100 to 90° in...
where h is the Use the Laplace transform to solve the following initial value problem: y"+y + 2y = h(t – 5), y(0) = 2, y(0) = -1, Heaviside function. In the following parts, use h(t – c) for the shifted Heaviside function he(t) when necessary. a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)}. L{y(t)}(s) = b. Express the solution y(t) as the...
Please solve both questions please. Solve the given initial value problem. y'"' + 11y'' + 38y' + 40y = 0 y(0)= 0, y'(0) = 10, y''(O) = - 72 y(x) = Find a general solution for the given differential equation with x as the independent variable. y(4) + 6y'' +9y = 0 A general solution with x as the independent variable is y(x) =
exact differential equations 2. Solve the initial value problem: (2.1 – y) + (2y – r)y' = 0) with y(1) = 3. 3. Find the numerical value of b that makes the following differential equation exact. Then solve the differential equation using that value of b. (xy? + br’y) + (x + y)x+y = 0
2) (a)(10 pts.) Find the continuous solution to the initial value problem de + y = 9(2) where q() = { 0 if 2>1 sat S 1 if |2<1. satisfying y(0) = 0. (b)(10 pts.)Solve the differential equation de ty