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6 (5) Solve the differential equation using a Laplace Transform: y 3y' +2y t y(0) 0, y'(0) 2
Solve the Following: 2y'' + y'+ 2y = u5(t) − u20(t) y(0) = −1 y 0 (0) = 3
Determine whether the equation is exact. If it is, then solve it. 4e+(2y – t)dt + (3 + 8 e") dy = 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. = C, where is an arbitrary constant. O A. The equation is exact and an implicit solution in the form F(t,y)=C is (Type an expression using t and y as the variables.) O B. The equation is not exact.
2. Use the Laplace Transform to solve the initial value problem y"-3y'+2y=h(t), y(O)=0, y'(0)=0, where h (t) = { 0,0<t<4 2, t>4
Find the particular solution such that y=0 when t=0 of the differential equation: (dy/dt) - 2y = t
Solve the initial value problem y" + 3y' + 2y = 8(t – 3), y(0) = 2, y'(0) = -2. Answer: y = u3(t) e-(-3) - u3(t)e-2(1-3) + 2e-, y(t) ={ 2e-, t<3, -e-24+6 +2e-l, t>3. 5. [18pt] b) Solve the initial value problem y' (t) = cost + Laplace transforms. +5° 867). cos (t – 7)ds, y(0) – 1 by means of Answer:
Solve for y(t). dy/dt + 2x = et dx/dt-2y= 1 +t when x(0) = 1, y(0) = 2
2y + y + 2y = g(t), (O) = 0, y'(0) = 0 where g) 5 St<20 10, 0<t<5 and t > 20
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U. + 2y + y + 1 -e: y(0) = 0, y'(o) - 2 In Problems 31-36, determine the form of a particular solution for the differential equation. Do not solve. 31. y" + y = sin : + i cos + + 10' 32. y" - y = 2+ + te? + 1221 x" - x' - 2x = e' cos - + cost y" + 5y' + 6y = sin t - cos 2t 35. y" –...
5. (13 pts) Solve the following initial value problem: y" + 2y' + y-ul (t)o V"(0) 0. y(0) 0, (t-1), -(t1) cos