b) Find v²f where f = e²x sin2y. cl Write the sufficient condition for ovistence of Lapla
b) Find v²f where f = e²x sin2y. cl Write the sufficient condition for ovistence of Lapla
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
solve b
![a) Find the Laplace transformation of the function f(t) = cosh at sinh bt
b) Find V2f where f = e2x sin2y.
c) Write the sufficient condition for existence of Laplace transformation of a
function.
d)
Find the Directional derivative of the function f = x² + y² at a point p (1,1) in
the direction ä2î - 4j
e) State Green's theorem in plane.
f)
Find the Laplace transformation of the unit impulse function
8(t-22017) and The unit step function U(t-22017)
g)
Find the Fourier sine series of the function f(x)=-100¹0(-n < x <n);
f(x)= 100¹0(0<x<n)
h) Find a parametric representation of the Parabolic equation
z = 9(x² + y²)
(1; 0 < t < 1
i) Find L[f(t)]. Where f(t) = 2; 2 <t<4
(0;
t> 4
j)
Find the value of L-1
s²+6
[(s²+1)(s+4)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23136dec-6537-43e6-8746-1a685f496696%2F6a006a08-b2f8-44ac-ab3b-20083c836710%2Fv1xakj8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) Find the Laplace transformation of the function f(t) = cosh at sinh bt
b) Find V2f where f = e2x sin2y.
c) Write the sufficient condition for existence of Laplace transformation of a
function.
d)
Find the Directional derivative of the function f = x² + y² at a point p (1,1) in
the direction ä2î - 4j
e) State Green's theorem in plane.
f)
Find the Laplace transformation of the unit impulse function
8(t-22017) and The unit step function U(t-22017)
g)
Find the Fourier sine series of the function f(x)=-100¹0(-n < x <n);
f(x)= 100¹0(0<x<n)
h) Find a parametric representation of the Parabolic equation
z = 9(x² + y²)
(1; 0 < t < 1
i) Find L[f(t)]. Where f(t) = 2; 2 <t<4
(0;
t> 4
j)
Find the value of L-1
s²+6
[(s²+1)(s+4)]
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