Department: Student Id Number : Student Name : 1. Consider the joint PMF Px (x,y) given in the following. Px(x.y) x= 0 x = 1x=2 0.22 0.29 0.06 0.15 0.19 y = 1 0.09 y = 2 2. Assume the joint PMF Px (x,y) given in Problem 1. (a) Find Px(x). (c) Find P[X>Y]. (b) Find Pr(v). (d) Find E[X].

Q: 3 3 If / f(x) dx = 14 and f(x) dx = 12, 2 then find f(x) dx. Select one: А. 2 ОВ. 22 О С. 6 D. 8 E.…

A: Given; integration of f(x) limit from 1 to 3 equal to 14 and integration of f(x) limit from 2 to 3…

Q: 1. find the linear approximation to /(x) at x = Xg. Use the linear approximation to estimate the…

A: Linear approximation

Q: 2. Solve for y in terms of X for the following equations: a) In(1- 2y) = x b) In(y- 1)- In 2 = x +…

A:

Q: iv) if zx = (y)¯1 then zx/Zy %3D

A: We have to find          zxzy where , zx=(y)-1 If ,   z=z(x,y)  then,∂z∂x= derivative of z with…

Q: dx 2. Find the value of at y=1 if x=z³+4z and z= (y² + 2y)²/³. dy

A: We have to use chain rule while differentiating.

Q: ) (2х +1) 3 —) (х+2у) — 1,. - 4x + 2у.

A:

Q: [y] + √2x+3] dx = (2x+3)dy, y(-1) = O

A:

Q: 1. (x2 + y² + 1)dx + x(x-2y)dy = 0 (Non-exact Equation) Ans: x² - y² + xy - 1 = cx

A:

Q: 4. y(y² - 2x²) dx + x(2y² - x²)dy = 0 [Answer: x²y² (y² - x²) = = C

A:

Q: S(y* - y-3)dy

A:

Q: 2xydy + (y- 3x-)dx = 0;y(3) = 2 O xy² - x³ = c O x³ 2 – xy² = -15 Ox* - xy? = 15 O x³- xy? = c

A:

Q: 6. f(x)= x³ - 4x g(x) = V2x h(x)= 2x+3 %3D %3D Find (h°g)(72) a. b. (h°h)(-4)

A:

Q: Q3. Verify that y² = x² – 3 is the particular solution to the following ivp: y' = ; y(2) = -1. %3D

A: To check whether a solution is particular solution to ivp , it must satisfy the differential…

Q: Examplei- Let F 4)= tittjt Sintk then find a)

A: Given,           F→t=ti+t2j+sintk

Q: %3D =D3e %3D 4.

A:

Q: If z = x2 – xy + 4y2 and (x, y) changes from (1, –1) to (0.96, –0.95), compare the values of Az and…

A: We have to use differential to find results.

Q: 8. (y2 + 7xy + 16x²)dx + x²dy = 0,when x = 1, y = 1

A:

Q: Is y = cīt + cf is the solution to y" – 12y = 0? Prove it

A:

Q: Solve the following: cInc y(1+V3+y2)y' with y(1) = -1. Do not solve explicitly for y. That is, you…

A:

Q: F. If F = CC) + 32 then 65 °C = %3D %3D

A: We have to find the °F

Q: 4. Suppose y satisfies the equation = 3y. Also when x=0, y=0, then which of the followings dx can be…

A: An initial value problem is an ordinary differential equation with an initial condition which…

Q: 2. Solve the following DE x y" – 4y = x e

A:

Q: 3. (2x2 + 2)dy + xydx = 0

A: (2x2 + 2)dy + xydx = 0

Q: 10. use "Bernoull's Equation" method dy -y= ey! dx

A: The given problem is to solve the Ordinary differential equation using Bernoulli equation method, we…

Q: Solve the following D.Es: 1. (x + 1) = x(y² + 1).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.