Solve the following initial-value problems: (a) 2- (b) (c) dx dt (e) dx dt dx dz (d)

Solve the following initial-value problems:

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(a) 2- (b) (c) dx dt (e) dx dt dx dz (d) 9- dx dr dx dt + d.x - 2- dx dr x(0)= 1, dt dx dt 5 d.x dt d.x + 4x=0, x(1) = 0,(1)=2 dt d.x dx +6+x=0, x(-3) = 2,(-3) = // dt dt + 6- d.x + 3x = 0, x(0) = 1, (0) = 0 dt d.x + 8x = 0, x(0) = 1, (0) = -2 dt dx dt dx dt d.x +11- ,dx dt dt - -(0) = 0, 6x = 0, dx dt (0) = 1 d.x + 12 + 8x = 0, dt d.x dx x(1)= 1, (1)= 1, (1) = 0 dt