Laplace transform using differential equations

Click For Summary
SUMMARY

The discussion focuses on the application of Laplace transforms in solving differential equations, specifically addressing the derivative of a function with respect to the Laplace variable 's'. The user presents a problem involving the function Y(t) = sin(sqrt(t)), with initial conditions Y(0) = 0 and Y'(0) = infinity. A key point of contention is whether Y'(0) can be treated as a constant during differentiation, with participants concluding that while Y(0) and Y'(0) are constants, the treatment of infinity requires careful consideration.

PREREQUISITES
  • Understanding of Laplace transforms and their applications in differential equations
  • Familiarity with initial value problems in calculus
  • Knowledge of limits and differentiation rules
  • Basic understanding of trigonometric functions and their derivatives
NEXT STEPS
  • Study the properties of Laplace transforms in relation to initial conditions
  • Explore the concept of treating infinity in calculus and its implications
  • Learn about the differentiation of functions with respect to parameters in Laplace transforms
  • Investigate the application of Laplace transforms to solve specific types of differential equations
USEFUL FOR

Students and professionals in mathematics, engineering, and physics who are working with differential equations and Laplace transforms, as well as educators teaching these concepts.

Belgium 12
Messages
40
Reaction score
0
Hi members,

Laplace transform using differential equations.(see attached PDF file)

My question d/ds(s^2 y- s Y(0)-Y'(0).)...
Y(t)=sin(sqrt(t)) Y(o)=0
Now Y'= cos(sqrt(t)/2sqrt(t) Y'(0)=infinity

d/ds (Y'(0)=?? can it be treated as a constant or can we change limit and differentiation??I don't think so.
like d/ds (cos(sqrt(t))/2sqrt(t)=0

Thank you
 

Attachments

Physics news on Phys.org
Belgium 12 said:
Hi members,

Laplace transform using differential equations.(see attached PDF file)

My question d/ds(s^2 y- s Y(0)-Y'(0).)...
Y(t)=sin(sqrt(t)) Y(o)=0
Now Y'= cos(sqrt(t)/2sqrt(t) Y'(0)=infinity

d/ds (Y'(0)=??
Y(0) and Y'(0) are constants, so their derivatives are both zero.
Belgium 12 said:
can it be treated as a constant or can we change limit and differentiation??I don't think so.
like d/ds (cos(sqrt(t))/2sqrt(t)=0

Thank you
 
Hello Mark 44,

If I understand it,Y'(0)=infinity.Here infinity can be treated as a constant.

Thank you
 

Similar threads

MHB Solve integral with laplace transform
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Laplace transform in spherical coordinates
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad On convolution theorem of Laplace transform: Schiff
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad On (real) entire functions and the identity theorem
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Laplace transform of an expression using transform tables
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Landscape Fabric Roll
  • · Replies 8 ·
Replies
8
Views
3K
MHB Solving PDE using laplace transforms
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Problem with calculating projections of curl using rotation of contour
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Inverse Laplace transform of a rational function
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Lipschitz continuity of vector-valued function
  • · Replies 3 ·
Replies
3
Views
4K