In Problems 2 to 9, use Laplace transforms to solve the given differential equations. dy dy 2. 9 - 24- dr2 +16y=0, given y(0)=3 and dr y'(0)=3. y= the (y=03-14 3. dx +100x=0, given x(0)=2 and dt2 4. x'(0)=0. [x=2 cos 101] dzi di +1000 +250000=0, given d2 dr i(0)=0 and i'(0)=100. [i=100+ e -5001 2x dx +6 +8x=0, given x(0)=4 and dt r'(0)=8. [x =4(3e-21 - 2e-41) 5 5. d12 2 6. dy dy -2 + y=3e4x, given y(0) = == dr2 dr 3 and y'(0)=43 - 1et = (4x - 1)e +