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(Solved): 15:00 Vol) 4G+ L 19% note that an the questions win de marked thereiore, it is migny recommended ...
15:00 ® Vol) 4G+ L 19% note that an the questions win de marked thereiore, it is migny recommended to attempt an or them. Question 1 Solve the following initial value problem using Laplace transforms
y^('')-7y^(')+10y=9cost+7sint,y(0)=5,y^(')(0)=-4Question 2 Calculate the Laplace transform of the following functions (2.1)
e^(-2t)cos4t. (2.2)
(2t+1)U(t-1).
\int_0^t e^(-\tau )cos\tau d\tau (2.4)
te^(2t)sin6t(2.5)
t^(2)U(t-2)26 APM2611/101/0/2025 (2.6)
t\int_0^t \tau e^(-\tau )d\tau Question 3 Calculate the following inverse Laplace transforms
L^(-1){(2s-4)/((s^(2)+s)(s^(2)+1))}
L^(-1){(e^(-\pi s))/(s^(2)+1)}
L^(-1){(e^(-3s))/(s^(3))}
L^(-1){(2s+4)/((s-2)(s^(2)+4s+3))}Question 4 Use separation of variables to find a solution of the partial differential equation
x(delu)/(delx)+tany(delu)/(dely)=0on
xin(0,\infty )and
yin(0,(\pi )/(2)), with boundary value
u(x,(\pi )/(2))=x.
(delu)/(delx)=4(delu)/(dely);,u(0,y)=8e^(-3y)