dx dy %3D 2x + 2) + 1 dr dt dx +2 dt J+ 3 dt

Q: dx 8х — 9у dt dy = x + 2y x(0) = 2 y(0) = 1 - dt

A: The solution is given as

Q: .dx/dt = x+y², dy/dt = x + 2y

A: We have to find the critical points of the given system of equations dxdt=x+y2 ,dydt=x+2y

Q: 13 x2. dx 3 у — ху, у(-1) %3D —1 dy 14 + 2у %3D 1, у(0) %3D3 dt

A: A differential equation is an equation in x,y and derivatives of y. Initial value problem is a…

Q: d'y +45 - 6y = -12 ; y (0) = 1, y (0) = 4, y" (0) = -2 %3D %3D dt3 dt? dt

A: We have to find the solution.

Q: dx = 3x + 2y dt (a) dy 4x + y | dt

A: a Let X'=AX where x=xy , A=a11a12a21a22Equilibrium point:-1 Node →  λ1,λ2 are real number of the…

Q: dx = x(1 – y) dt dy у(х — 1) dt

A: Solution of the problem as follows

Q: Dx+Dy= ムxy43t Dx-Dy =-2x+2y %3D

A:

Q: dx dy - 2x – 2y. a) dt -x, dt dx = x + 3y, dt dy dt 2.x. b) dx dy (c) 3x – 4y, 2x – y. - dt dt

A:

Q: d²x + 2x = y dt? d?y +2y x dt2 d) x'(0) = y'(0) = 0

A:

Q: d'y dt? dy - +6y = 21° –t +3 ; y(0)=1, dy -(0) = 2 dt -5 %3| dt

A: At first, we have to find the complete primitive (C.F.) and then we find the particular integral…

Q: Find dy/dx. x = t, y = 9- 2t %3D x3x dy dx I3D

A: Given equations:            x=t2,   y=9-2t

Q: dx -Зх — бу 3D 0 dt dy 3x + 3у %3D 0 dt

A:

Q: dy - 2y = 0, x(0) = 4, y(0) = 0 dt dx --x - 2y = 16te', 2x – dt

A:

Q: dx -y = 5 dt dy = 3t dt 2x -

A:

Q: d y dy 14. dt2 +2, + y= 2 cos 2t dt У (0) —D у (0) — 0

A:

Q: 8x – 2y f(x, y) %3D 7x2 + 5y dy? dxðy dydx

A: Using partial derivative rules

Q: d²y dy 2 + 2 - y = 0 dt2 dt ك إضافة ملف

A:

Q: (dx = x - y+z dt |dy = x +y – z dt dz — 2х — у dt

A:

Q: d?x dy -y = 0, dt? dt dx 2- dt dz +- z = 0, dt dx dy + 3x + dt -4y+ 3z 0; dt dx x(0) = 0, (0) = = 1,…

A:

Q: dx | | dt dy dt dz dt 2x + y + 2z 3.x + 6z = -4x – 3z - =

A: Given: The differential equations are  dxdt=2x+y+2zdydt=3x+6zdzdt=-4x-3z To find the general…

Q: dx dy 5et %3D dt dt

A:

Q: dx = 3x + 2y dt dy -2x + 3y dt

A:

Q: d³y dt3 dy + 4 dt2 + 5 dt + 2y = 10 cost y(0) = 0, y'(0) = 0, y"(0) = 0 %3D

A:

Q: integrate the following ∫(y-2 + 1/2y - 1)dy

A:

Q: 7. x = (t + 1)(t + 2)(t + 3), dx dt 8. y = (; ++), 1 +5). dy %3D x2 x3 dx

A:

Q: dx 3x 6y = 0 dt dy 3x + Зу %3D 0 dt

A:

Q: dx + 2– + x = u(1) x(0) = x'(0) = 1 dt

A:

Q: d dt dx dy ruations dt - 2x +2y 1-2t, dyx-0. Giv dt 2 dt

A:

Q: D²x – Dy = t x(1) = 1, y(1) = 0, D = 4. %3D (D + 3)x + (D + 3)y = 3 dt

A: Here, it is understood that :               ; Now , by question , we get :…

Q: d2x/dt2 + 4dx/dt + 4x = 0   x(0) =2, x' (0) = 1

A:

Q: 1) [ (2t–1)² dt 2 2 2) dx X 3) [ , x(x² + 1)° d.

A:

Q: dy + 4y 2 e- 4e, y(0) = 0 dt %3D %3D

A: As you have posted multiple questions so according to our guidelines I answered only first question.…

Q: dx dy dy Find and dt' dt dx x = 3t – 3ln(t), y = 4t2 – 4t-2 dx dt dt dr

A: Given x=3t-3lnt        y= 4t2-4t-2

Q: 1 dy t dt -4y + 6 %3D

A:

Q: 꾸dz + Pdy =0, y(-1) %3D2. (3-y) dx + (y 2x) ry²

A:

Q: dx/dt = X +y dy/dt = 2x + 2y

A: To solve dxdt=x+ydydt=2x+2y

Q: dx : 2x-y dt %3D dy 3x - 2y + 8t %3D dt

A:

Q: dx a. dt b. 2y dt

A: A)  given equation can be written as (D-5/2)X -2Y =0 -3X/4 +(D+2)Y =0  By using elimination method…

Q: dx + 2x + + 6y = 2e' dt dt dx 3x +3. dt 2.+ + 8y = -1 dy dt

A: The given equation can be re- written as:

Q: の そ ニ ゼdd + とd dt :d と の まdと +(そ-乳)よy:。

A: As per the company's guidelines, we are supposed to solve first three sub-parts for you, kindly…

Q: dx dt dy dt x + 2y -2x – 3y x(0) = 1 y(0) = 2 | |||

A:

Q: dx +x= e', dt dt %3D

A: In the given question we have to find function x and y.

Q: dx + 2x – 3y = t dt

A:

Q: dx (b) (t– 2) – x = (t – 2)' , x(4)=10 dt dx (c) +5x -t = e" , x(0)= dt

A: Here we have to solve given initial value problem b and c.

Q: d’y -4 dy +y=t²-2t +3 1. dt? dt

A: The given differential equation is; d2y/dt2 -4dy/dt +y=t2-2t+3. Repost the next part.

Q: @ cDx -4D Dy +5 Dx Dy -zBj)u= e +2x -2x u= 中iyとx)+中2(当十×)+x43しy+x)+x. 3+2x 36

A:

Q: dw t- dt dw + x- dx 1, -0 1, w(х, 0) %3D f(x). ||

A:

Q: d'x dt? de - 4x =0 ,x(0) = 1,(0) = 2 di dt

A: Follow the steps.

Q: dx = x – 2y + 1 dt dy = x + 3y – 9 dt

A: given

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!