1. Find the inverse Laplace transforms of the following function: F(s) 58 +2 (8 + 1)(s+ 2)² 2. Obtain the inverse Laplace transform of the following function: 3. Solve the differential equation F(s) = = 5e-8 8+1 4. Solve the differential equation +3x+6x=et, x(0) = 0, r(0) = 0 5. Solve the following differential equation: +2x=d(t), x(0-)=0 *+2+5=0, z(0) =0, r(0)=3 6. Solve the following differential equation: x+2(x+w²x = 0, x(0) = a, x(0) = b where a and b are constants. (Additional condition: 0 <<1)