The general solution for uz + Uyy = 0, %3D u(r,0) = 1, u(z, 1) = 0, u(0, y) = 0, u(1, y) = 0 is O Elen sin(nz) + bn cos(-nz)] sin(ny) O Elan sin(naz) + bn cos(-nAT)| sin(nny) OElen sin(nxz) + bn cos(-nA2)| sin(nny) Olene + bne sin(nay) O n sin(ny) + bn cos(-ny)| sin(na) OE eze™ + bye sin(nz) 01. c be sin(ny) sin(nar)

Q: Show that u(x, t) = 4 tan-1 I-ut ev where v is constant, is solution of Uxz – Utt = sin(u)

A: To check the given solution satisfy the given partial differential equation, substitute the solution…

Q: 7- y" + 4y = cos x, y (0) = 0, y(n) = 0

A:

Q: عو + Y¹" + 3 Y" + Y' + 22 = 0 general Solution : Y = C₁ cos ax + C₂ Sinba + exp(-22) (C₂ Cos √ 1+1…

A: The auxiliary equation

Q: Find y' where y = tan(11a? + 8) v173 + 17 Answer: 51a2 y/ = sec2 (22æ)\/172³ + 17+ tan(11a² + 8)…

A: I have used the rule for composition of function and multiplication of functions

Q: 6. (a) Recall that sin z = ¹2; cos z = (i) Find real and imaginary parts of sin z and cos z, for z =…

A: Note : '' As per guidelines we will solve first three subparts. If you want any specific subpart to…

Q: 9) (D-1)y e' sin e+ cose. Ans.: y=Ce+Ce-e' sine".

A: Since you have posted multiple questions.. We are suppose to give solution of first one only...…

Q: z cos(2x)) - cos(2x))+

A: here using sin2x = 2sinxcosx                 cos2x = 2cos^(2) x -1

Q: he general solution of y" +

A:

Q: e cosl – i e™ sin 1 + e¯ cos 1 - i e- sin 1 2 e cosl + i e™ sin 1 – e- cos 1 + i e¯I sin 1 -TT 2 e…

A: Simplify the given expression: Coshπ-i

Q: (x + siny - cosy + 1) dx + (xsiny + xcosy)dy = 0

A:

Q: How did he get the value inside the circle f(x, y)=x² + sin(xy) Vf=x*+sin(xy)) i+ d(x²+sin(xy)), dx…

A: given ∇f(1,0)=2i+j we have to find the direction in which the directional derivative has some value.

Q: ㅠ [sin(y) sin sin (y) sin² (y) 1+ cos(y) dy KIN

A: We will use substitution method to integrate.

Q: Find y @) y ² y's SX-2 Sin (x) b) 2 Y = 2 cos (x)-x

A: To find the derivative each of the following functions. (a) y=5x-2 sinx (b) y=2 cosx-x2

Q: linear or not linear? 1) dy 1ax +exy = x²4² dx 2) y + e* sinx= x³y² 31 y\nx - x²y = xy! 4) dy + cosy…

A:

Q: tan x= Sin 2X

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

Q: معادله دیفرانسيل جواب عمومی Scul plas (2xy sin²x)y' + x³ + xy² sin 2x + y²sin²x = 0 y? cos 2x + 4 .a…

A:

Q: sin 8- + jG+1) sin² (@) = k² (27) sin e. and, (28) Z dộ? Show that equation (27) combined with…

A: given equation 1TsinθddθsinθdTdθ+jj+1sin2θ=k2        ...27 and 1Zd2Zdϕ2=-k2       ...28 use equation…

Q: 4) Find ôw/ ôr if w= (x+y+z)*, x=r-s, y = cos(r+s), z = sin(r + s) the point (r,s)= (1,-1)

A: Given - w = x + y + z2 , x = r - s, y = cosr + s, z = sinr + s To find - Find ∂w∂r at the point r, s…

Q: Find dy dx? A) y = 3sin u - sin'u and x 3 cos u- cos'u

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

Q: dz If Z = x' sin(y), x = s²t³ and y = s°t2, %3D ds a) None of these b) 6st³ x² sin(y) – 3s²t²x³…

A: Given query is to find indicated derivative.

Q: Q2/ Find ow/or if w = (x+y+z)³, x=r-s, y = cos(rs), z = sin(r + s) at the point (r, s) = (0,1)

A:

Q: c) f(x)=tan(cos².x) 11 COS X 1+ sin.x Dy=- b) y = 2

A: e)  f(x)=tan(cos2x)  f) y=cosx/(1+sinx) g) y=ex^2/x3 Repost the next part.

Q: Q9: If F(x, y, 2) = [sinh-(sin- (In (/sin(cos(x²)) y? + zyx + y, find and ду az Q10: If z =…

A:

Q: Find dy: dx 1) y = = = tan // -1/3 333 2 y = sec¹ 5x 3) y = cos cos2x 4) y = cot" ¹ 2 ² + tanı X/N…

A:

Q: dy z = 3e*S, y = 3z2 + sin(z) S i5I dx %3D

A: Given,           z=3ex and y=3z2+sinz

Q: fze [sin(3x)]-m(x, y, z), where m(x, y, z) = Part C. yz-1 %3D

A:

Q: 1. у" - 2y' %3D sin 4x

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.