Problem. Show that S {₁ 【 (s − 2)(s − 3)(s — 6) J L-1 -6)} = 1/2 ²² - e³t + e

Q: 1 s(s+1) 6) L'

A: Given: L-11ss+13

Q: If (In x)2 c (a (In x)? + b in x +c) + constant, then 2 a + 28 b + 18 c = 32

A: Solving the above given integral

Q: dx √8-2x-x² S=

A:

Q: 1. (x + √y² + 1) dx · (y – H.W. solve the following D.E. xy - - √12241) dy = 0

A: Step 1:

Q: 1. Solve for P given P' = 6t√P √² +3 with P(1) = 25.

A:

Q: 4. S (x + 1) √2x − 1 dx

A:

Q: 1. Find the value of k so that the ODE (y³ + kxy¹ − 2x) dx + (3xy² + 20x²y³)dy = 0..

A:

Q: 12 cos√(√x+4 dx

A:

Q: 8y dy e2y

A: topic - definite integral

Q: 2y" - 5y' + 3y = 14te²¹

A:

Q: 3. Find all possible values of k if "(2x + 4) dx = -12

A: Given integral is as below:

Q: dy 3 (113) _1) dri Ber roullis Solve this by using caruation. %3D

A: The equation is given by: dydx=31313-1 Assume x=1,y=3 to get: dydx=yxy13-xdydx+xy=xy14 Which is a…

Q: 353. y = x-1/2 (x² + 3)2 (3x – 4)ª

A: First, we expand the given expression using properties of logarithm