Assignment 2 Problems

Assignment # 2 (Problems) Ex. 4.4 Use Laplace transform to solve the integral equation 37: t

f (t ) + ∫ (t − τ ) f (τ )dτ = t 0

Ex. 4.5 Use Laplace transform to solve the integral equation 2: y '+ y = δ (t − 1), y (0) = 2 3: y ' '+ y = δ (t − 2π ), y (0) = 0, y ' (0) = 1 4: y ' '+16 y = δ (t − 2π ), y (0) = 0, y ' (0) = 1 6: y ' '+ y = δ (t − 2π ) + δ (t − 4π ), y (0) = 1, y ' (0) = 1

Ex. 4.6 2: dx = 2 y + et dt dy = 8x − t dt x(0) = 1, y (0) = 1 3: dx = x − 2y dt dy = 5x − y dt x(0) = −1, y (0) = 2 4: dx dy + 3x + =1 dt dt dx dy −x+ − y = et dt dt x(0) = 0, y (0) = 0

8: d 2 x dx dy + + =0 dt 2 dt dt d 2 y dy dx + −4 =0 2 dt dt dt x(0) = 1, x' (0) = 0 y (0) = −1, y ' (0) = 5 11: d 2x dy + 3 + 3y = 0 2 dt dt 2 d x + 3 y = te − t dt 2 x(0) = 0, x' (0) = 2 y (0) = 0 15(b):

di2 + Ri2 + Ri3 = E (t ) dt di L2 3 + Ri2 + Ri3 = E (t ) dt R = 5Ω L1 = 0.01 h L1

L2 = 0.0125 h E = 100 V i 2 (0) = i3 (0) = 0