Question

B. Evaluate the following definite integrals.
1. ​

Answer 1

Answer:

Find the Laplace transform of the function te sin 4t +

2.

1

Iy

dy

2. Solve the differential equation r

+ 2y = r tan(log ).

do

3. Solve the partial differential equation (I + y)p+ yq = 2 + .

3

4. Evaluate the definite integral

4. Evaluate the definite integralſ

de by using contour integration

3 90s

5. Solve the partial differential equation 2 ry: pr’y + gry + 4p.

6. Find the Laurent's series expansion of the function to

lone 2) about the

B

point == 2 If I ule-2" 22-2

is the Laurent's series expansion of fe then find

2

7. Solve the differential equation (D-- 12D+36) y = 2*+(1+1), which satses the conditions

y(0) = -1.7(0) = 2.

8. Find a power series solution in powers of r for the following differential equation

3

Y" - 2ry' + 3y = 0.

9. Using Cauchy's integral formula, evaluate the integral / me -ds, where h(e) = 3 - + 1 and

C is 1:= 1

10. Solve the following initial value problem by using Laplace transforms method

+ 6y + 16y= e ", y(0) = 1, y'(0) = -1.

STA

Answer 2

Answer:

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