- 008311. Find the Laplace transform of the function te sin 4t +2.1Iydy2. Solve the differential equation r+ 2y = r tan(log ).do3. Solve the partial differential equation (I + y)p+ yq = 2 + .34. Evaluate the definite integral4. Evaluate the definite integralſde by using contour integration3 90s5. Solve the partial differential equation 2 ry: pr’y + gry + 4p.6. Find the Laurent's series expansion of the function tolone 2) about theBpoint == 2 If I ule-2" 22-2is the Laurent's series expansion of fe then find27. Solve the differential equation (D-- 12D+36) y = 2*+(1+1), which satses the conditionsy(0) = -1.7(0) = 2.8. Find a power series solution in powers of r for the following differential equation3Y" - 2ry' + 3y = 0.9. Using Cauchy's integral formula, evaluate the integral / me -ds, where h(e) = 3 - + 1 andC is 1:= 110. Solve the following initial value problem by using Laplace transforms method+ 6y + 16y= e ", y(0) = 1, y'(0) = -1.STA​