\\(x\'=12x+5y\\) \\(y\'=-7x+e^(5t)\\) x(0)=0 y(0)=0 Let X(s)=L(x(t)), and Y(s)=L

Question

     (x'=12x+5y)         (y'=-7x+e^(5t))     

x(0)=0

y(0)=0

Let X(s)=L(x(t)), and Y(s)=L(y(t))Let  X(s)=L{x(t)}, and Y(s)=L{y(t)}.

Find the expressions you obtain by taking the laplace transform of both differential equations and solving for Y(s) and X(s): Find the expressions you obtain by taking the Laplace transform of both differential equations  and solving for Y(s) and X(s):

X(s)=

Y(s)=

Find the partial fraction  decomposition of X(s)  and Y(s) and their inverse Laplace transforms to find the solution of the system of DEs:

Find the partial fraction decomposition of X(s) and Y(s) and their inverse Laplace transforms to find the solution of the system of DE's:

x(t)=

y(t)=

Explanation / Answer

sX=12X+5Y

and

sY=-7X+1/(s-5)

So

on solving we get

sY=1/(s-5)-35Y/(s-12)

So

Y=(s-12)/((s-5)(s^2-12s+35))

and

X=5/((s-5)(s^2-12s+35))

So

Y=(s-12)/((s-5)(s^2-12s+35))

=1.25/(s-5)+3.5/(s-5)^2-1.25/(s-7)

So

y(t)=1.25e^(5t)+3.5te^(5t)-1.25e^(7t)

and

X=5/((s-5)(s^2-12s+35))

=-1.25/(s-5)-2.5/(s-5)^2+1.25/(s-7)

So

x(t)=-1.25e^(5t)-2.5te^(5t)+1.25e^(7t)

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.