Solve PDE 1 = e=*t u. u̟ =e¯*t Xx k (o0) u(0,t) =0 u(L,t) = 0 u(x,0) = L -x?

Q: dx 1)y /sec(3x) 2) y = Vu + 2u , x= u? - 3u

A: Definition used -            Chain rule of derivative -                             ddx(f(g(x))=…

Q: 3 tanx dx 3/ secx

A: Indefinite integral: An integral which does not have any upper limit or lower limit of integration…

Q: (v) er-y de +e**"dy = o

A: We will solve the differential equation by the method of separation of variables.

Q: L, x*e*** dx 3+1

A: 3.1) ∫-12x2e(x3+1)dx Let u=x3+1 du=3x2dx

Q: 4x−³+2 3 8. S ² X - 2 - X dx

A: Given :∫4x-3+2x-2-xdx

Q: find the pauticuler soluhion fr + loy = x'_e*sin(8x)

A: Solve particular integral in above differential equations.

Q: xe*dx 4. S (1+x)?

A: Given data: The given integral is ∫xex1+x2dx. The given integral can be written as,…

Q: d/dx [x/(x^2 + y^2) ] = * O [(y^2 + x^2)/(x^2 + y^2)^2 ] O -[(y^2 +x^2)/(x^2 + y^2)^2 ]…

A:

Q: k xy' - y = x*y"

A:

Q: e"+e (1) V 23 + 1 dx by speculation . x=e"+e-T (2) Use (1), if necessary, to evaluate L +1 (-) de V…

A:

Q: (? + 5 )2y = 3r(y² + 1)- -(a+ + 8x² + 9)y, y(1) = 0 4+8 (,? + 5),'

A: solve the given equation by separable method:

Q: Find * dy ,If y 3 dx + x O x^2 + x O x^3 + x^2 +1 O x^2 + x + 1 O 3x^2 + 2x + 1

A:

Q: S (sech*y – sec®y) dy

A: I =∫ (sech4y -sec6y) dyI=∫ sech4y -∫ sec6y dyI=∫ sech2y (1-tanh2y) dy       -∫ sec2y (1+tan2y)2…

Q: 3s+7, Find L'f 's2+9*

A:

Q: Find the artho gon al traje eteries to c°y" - 4y + x*

A:

Q: tan x= Sin 2X

A: Given: y'+y tan x= sin2x

Q: Show that A Yk= V' Yk+r

A:

Q: Σ(+r=1)a-my y=0 = (1 - (1 − π)^^) — -

A:

Q: If (2xy?+4) dx +2 (x*y-3) dy = 0 then ƏP/ay # ƏQ/ax *

A: Given: The equation is, 2xy2+4dx+2x2y-3dy=0 And ∂P∂y≠∂Q∂x To find: Whether it is true or false.…

Q: +ay'- - 3X = 0

A:

Q: and d^2y/dx^2 for

A:

Q: Solve Uxx = utt u(x, 0) = 0, "+ (x, 0) = x² '

A:

Q: 10. Integral 2-t dt

A:

Q: Substitute the value of y' in 1 + (y)²

A:

Q: 4. S V tan x sectx dx

A:

Q: 9. dx J1 (3x²+1)3

A:

Q: find dy/dx x(х+1)(х- 2) (х*+1)(2х+3) 25) у%3 43) у%3D 1+(lin x)? 1+(ln x)?

A:

Q: 6. (D² + 1)y = 10e* sin x

A: see below the answer and explanation

Q: dy + ydx %3D = 3x²y?dx,

A:

Q: 6. 2 I (ve**)dx dy у /2

A:

Q: 3 + .2 J(u) 4u + '(u) =

A: Given J(u)=(3u+3u2)(4u+4u)

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.