lab report for jack jones

1-a

>> syms t

y(t)=4+3*t+2*exp(-3*t)

laplace(y(t))

y(t) =

3*t + 2*exp(-3*t) + 4

ans =

2/(s + 3) + 4/s + 3/s^2

1-b

>> syms t

>> f(t)=2*exp(-4*t)+sin(6*t)

f(t) =

2*exp(-4*t) + sin(6*t)

>> laplace(f(t))

ans =

2/(s + 4) + 6/(s^2 + 36)

1-c

syms t

>> c(t)=5*t*exp(-3*(t-2))

c(t) =

5*t*exp(6 - 3*t)

>> laplace(c(t))

ans =

(5*exp(6))/(s + 3)^2

2-a

>> syms s

>> y(s)=2/s+6/(s+3)^2;

>> ilaplace(y(s))

ans =

6*t*exp(-3*t) + 2

2-b

>> syms s

>> f(s)=(s+2)/(s*(s+1))

f(s) =

(s + 2)/(s*(s + 1))

>> ilaplace(f(s))

ans =

2 - exp(-t)

2-c

>> syms s

>> c(s)=(4*s+6)/((s+1)*(2*s^2+12*s+16))

c(s) =

(4*s + 6)/((s + 1)*(2*s^2 + 12*s + 16))

>> ilaplace(c(s))

ans =

exp(-t)/3 + exp(-2*t)/2 - (5*exp(-4*t))/6

EX 3

1

>> syms x

>> dsolve('(2*D2y)+(12*Dy)+(10*y)=8','y(0)=0','Dy(0)=1')

ans =

4/5 - exp(-5*t)/20 - (3*exp(-t))/4

2

>> syms t

>> [i1,i2]=dsolve('(Di1)+(20*i1)-(10*i2)=100','(Di2)+(20*i2)-(10*i1)=0','i1(0)=0','i2(0)=0')

i1 =

exp(-30*t)*((5*exp(30*t))/3 + exp(20*t)*(5*exp(10*t) - 5) - 5/3)

i2 =

exp(-30*t)*(exp(20*t)*(5*exp(10*t) - 5) - (5*exp(30*t))/3 + 5/3)