2. Integrating factor Solve the given initial value problem. a) (1 + x*)y' + 2xy =...
4. Use the Laplace transform to solve the initial value problem y" + y = f(1) = -2, ost<2 13t+4, 122 y(0) = 0, y'(0) = -1
Use the Laplace transform to solve the given initial-value problem. so, 0 <t< 1 y' + y = f(t), y(0) = 0, where f(t) 17, t21 y(t) = + ult-
Question 4 < > Solve the initial value problem below. x+y'' - xy' + y = 0, y(1) = – 5, y'(1) = 0 y
Problem 2: Solve the initial value problem: with 4. 0<t〈2 f(t) 14t-2i,22
2) (10) Find the integrating factor and solve the initial value problem -2xy + y(1) Find an interval of solution w of cooling, the rate at which the temperature of an object isproportional to the difference between the temperature 3) (10) In Newton's law of cooling, the rate at whic changes over time is proportional to the of the object (t) and the temperature of the surrounding medium For the following problem set up the initial value problem, then solve...
Solve the y"+ 4y = initial value problem s 1 if 0<xsa To if x>,T ylo)= 1, g(0)=0
2. Solve the initial-boundary value problem 2% for 0 < x < 6, t > 0, u(0,t) = u(6,t) = 0 for t > 0, u(x,0) = x(3 - x) for 0 5736. (60 pts.)
(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) 6y 6xe-6x, 0 < x < 1 with initial condition y(0) = 2. Given the first order IVP y 0, х21 (1) Find the explicit solution on the interval 0 < x < 1 У(х) %3 (2) Find the lim y(x) = х—1 (3) Then find the explicit solution on the interval x 1 У(х) —
(1 point) Consider the following initial value problem: 4t, 0<t<8 \0, y" 9y y(0)= 0, y/(0) 0 t> 8 Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)} find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)