Use the Laplace transform to solve the following

Erika Bernard 2022-04-08 Answered
Use the Laplace transform to solve the following initial value problem:
y+y=2t
with y(π4)=π2 and y(π4)=22
You can still ask an expert for help

Want to know more about Laplace transform?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

llevochalecoiozq
Answered 2022-04-09 Author has 15 answers
Laplace-transforming both sides of y+y=2t
s2Y(s)y0sv0+Y(s)=2s2
Hence
Y(s)=y0(ss2+1)+(v02)(1s2+1)+2s2
Taking the inverse Laplace transform,
y(t)=y0cos(t)+(v02)sin(t)+2t
From the conditions y(π4)=π2 and y(π4)=22 ,we get
y0+v0=2y0v0=2
Thus y0=2 and v0=0, and
y(t)=2cos(t)2sin(t)+2t
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more