3. (6pts) Find a general solution of the problem. 1- y = { cost, where (t...
(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.)
Find the solution of the given initial value problem: y" + y = f(t); y(0) = 6, y'(0) = 3 where f(t) = 1, 0<t<3 0, įst<<
Q4 a) Find the general solution of the differential equation Y') + {y(t) = 8(6+1)5; 8>0. Y'8 8 >0. 8(8-1)3 b) Find the inverse Laplace transform y(t) = £ '{Y(3)}, where Y(s) is the solution of part (a). c) Use Laplace transforms to find the solution of the initial value problem ty"(t) – ty' (t) + y(t) = te, y(0) = 0, y(0) = 1, for t > 0. You may use the above results if you find them helpful....
a) Find the general solution of the differential equation Y'(B) + 2y(s) = (1)3 8>0. b) Find the inverse Laplace transform y(t) = --!{Y(s)}, where Y(s) is the solution of part (a). c) Use Laplace transforms to find the solution of the initial value problem ty"(t) – ty' (t) + y(t) = te", y(0) = 0, y(0) = 1, fort > 0. You may use the above results if you find them helpful. (Correct solutions obtained without Laplace transform methods...
Find a general solution to the given equation for t<0. y''(t) – Ły'(t) + 5 -y(t) = 0 t The general solution is y(t) = (Use parentheses to clearly denote the argument of each function.)
Problem 2: [Also challenging] Find the solution of the following IVP: y' +2y = g(t), with y(0) = 3 where g(t) = - 0<t<1: g(t) = te-2 > 1.
Find y(t) solution of the initial value problem 2 y2 +bt2 y'= y(1) = 1, t>0, ty
Find the general solution, y(t), of the differential equation t y" – 5ty' +9y=0, t> 0. Below C1 and C2 are arbitrary constants.
Find a general solution to the given Cauchy-Euler equation for t> 0. 2d²y dy +41 - 10y = 0 dt at² The general solution is y(t) =
Find y(t) solution of the initial value problem 3t y? Y' – 6 y3 – 4t² = 0, y(1) = 1, g(1)=1, t > 0.