Show that if Y = ax+ b (a ≠ O),then Corr(X, Y) =+1or -1. Under what conditions will p =+1?

Q: Q:Ifx = sin 6, y = 0,y= cos p6, prove that (1-x )y, xy,+ p°y= 0, dy and y1 d dy where y, %3! %3! de

A:

Q: 10. y = C, cos 4x + C2 sin 4x + C3xcos 4x + C4xsin x + C5; C, to C5 are arbitrary constants

A: Since their are 5 arbitrary constants so the differential Equations will be of order 5. We find the…

Q: I. Solve the heat o at with lot) - (2,t) 3TX 8TX aud Ulxio) = lo + 5 Cos - 3 Cos *

A:

Q: Find the particular solution of 9. 12+ 4y = 3x – 1 given that when x=0, y=0 and dx

A:

Q: If y = cos ¹ prove Zyy + z = 0. )Z = (1 + i)(2-1)-¹, find |Z|.

A: Here given y=cos-1(z/x). We prove that zyy+z=0.

Q: Find the general dafferential equatron (t) t 36y () - o lol00lution of the general solution y Co) =…

A:

Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y()= 3x?y² becomes +z(-÷) =…

A:

Q: O(y-+ rycota)dr + zdy O (coszcosy– cotz)dr sinrsinydy 0 O ydr + (3z -g')dy = 0

A: A differential equation is called linear if 1) every dependent variable and derivative involved…

Q: Let y(x) be the solution for the DE : y' = (x + y – 1)² If y(0) = 1, then find y()

A:

Q: Show that the equation 2²y Əy +2k 2²y 6x² ax² 1 2² Ət possesses solutions of the form X 00 kt Σ c,…

A:

Q: If u(t) = (sin(2t), cos(2t), t) and v(t) = (t, cos(2t), sin(2t)), use Formula 5 of this theorem to…

A:

Q: Find Duf at P. 3 4 f (x, y) = sin(3x – 4y); P(4,3); u = i j %3D - - NOTE: Enter the exact answer.…

A:

Q: Let z=xIn(x²+y²-e)-235xy, x=te, y=est. If the value of oz when s=2 and t=1 is equal to Ae?+Be", then…

A: Here, the given functions are: z=x lnx2+y2-e4-235xy, x=t es, y=est so, z is a function of x and y…

Q: ck that y(x) = e rx with r satisfying ar 2

A: Introduction: Introduction: In mathematics, differentiation is the process of determining the…

Q: The general solution of x*y = -x³y- csc(xy) is A 2x^сos(xy) - 1 %3Dсх B 2x?sec(xy)+1= cx…

A:

Q: B. Prove that the given equation is a solution to the given DE: 5. x= 2t + C; y = Ct + 3 ;…

A:

Q: Sc ot'(3y)dy

A:

Q: Find the formulation of a particular solution of y"+2y'+ 5y = t² +4t – t²e-t cos 2t without…

A:

Q: The general solution of y''+4y'= 0 is ° y = C, + C,x+ C,e* ° y = C,e* + C,e²* + C;e2* -4x y = C,e* +…

A:

Q: 2. Let R(t) = } sin 4t î – bcos“(21) j + 2t k. E

A:

Q: Solve. a) y - e" cosy b) +2y= + 2y 6e **-+(Let u - )

A: Since you have asked multiple subparts of this question, we will solve the first three subparts…

Q: x°y" – 3x'y"+ 6xy'– 6y = 0 -

A:

Q: Q3 Suppose that w = x² + y² + z² x = e" cos 0 ,y= e"sin0 ,z = re® aw аnd ar aw Find дө

A:

Q: if z sin とこ3r'+25 , Y=4イ-ス3 Z = 2r-35* W= Z Sin %3D * find aw,w ar me' me as

A:

Q: Verify that the indicătéd function is an exp for each solution. y" - 6y' + 25y = 0; y = e3x cos 4x…

A: Recall: (uv)'=u'v+uv' where u and v are the function of x

Q: and its solution EE{ Jm(VAmr) |amncos mô cos( /amict) m=Oh=1 и(r, 0, t) %3 + bmncos m0 sin(VAmict) +…

A:

Q: No type answer

A:

Q: The general solution of the DE: ZV=1 is y=x(x+ c) Select one: O True False

A:

Q: C) Find a z and of xy" ay (xy2) - -군3 COs %3D

A:

Q: What are the conditions on A, B and C for an ODE of the form Ay'' + By' + Cy = 0 to have solutions…

A:

Q: Find the solution of xy" + 5xy +(4 – Ix)y = 0, x > 0 of the form where co = 1. Enter n= 1,2,3, ...

A: Let the solution of the above differential equation is given as: y=xr∑n=0∞cnxny=∑n=0∞cnxr+nThe…

Q: 1. Solve for the othogonal trasctories y =x²(1-cx)

A:

Q: Let y, be a solution to y" + zy +r'y = cos (z) and y, be a solution to y" + zy' + z*y = sin°(z).…

A: Given that y1 be a solution of y''+xy'+x2y=cos2x and y2 be a solution of y''+xy'+x2y=sin2x. That is,…

Q: x²y"+xy'-y= x 2

A: Given Cauchy-Euler equation is x2y''+xy'-y=x.

Q: The auxiliary (charasteristic) equation of the DE x²y" + xy' + y = 0 is %3D

A: Euler-Cauchy type differential equation: Let a equation x2y''+y=0 ..(i) Put y=xm in the given…

Q: Determine c, and c2 so that y(x) = c, sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

A: Consider the function: yx=c1sin 2x+c2cos 2x+1. Calculate c1 and c2. Given yπ8=0 and y'π8=2.   Since…

Q: If f(z, y) = e sin 8y, then fzy is given by: O 16 e sin 8y 16 e sin 8y O 16 e cos 8y 27 16 e cos 8y

A: We can solve it by taking partial derivative of both side two times as below

Q: 2. (a) Determine c, and cz that y = c¿e³x + c2e¯2x + 2 sin x will satisfy the conditions y(0) = 0…

A: We have to determined the value of C1 and C2that y=C1e3x+C2e-2x+2sinx will satisfy the condition…

Q: Q6A)If y = cos ¹) prove Zyy + z = 0.

A: See this solution in below

Q: 2. Find te gunural soiUtion of 2

A:

Q: Given f(x.y) = e X cos y, Evaluate fx(2,0) e2 cos 2 O sin 2

A:

Q: The coefficient of r cos e in the general solution of U,+u,+u90 =0; 1<r<2,

A: In this question, we have given Laplace equation in polar form. Here we use the general solution of…

Q: If A = ze?xVi VxA at the point (2,0,3) is + 2xycosy j+ (x + 2y) k then the valueof

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

Q: EX~U(0,1) if Y= =L l(t-x)~ Exporential (A,

A: From the given information, X~U0,1 The probability density function for X is, f(x)=11-0       =1,…

Q: Verify that y(x) = erx, with r satisfying ar+b = 0 is a solution of the equation ay' + by=0.

A:

Q: Determine cı and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

A:

Q: x²y" – 4xy'+6y= 0, y(2)= 0, y'(2)= 4 %3D -

A: Given differential equation is: x2y''-4xy'+6y=0           y(2)=0; y'(2)=4 In Cauchy Euler method we…

Q: For u = ex cos y,(a) verify that ∂2u/∂x∂y = ∂2u/∂y∂x;(b) verify that ∂2u/∂x2 + ∂2u/∂y2 = 0.

A: The given  function is, u=excosy (a) To verify ∂2u∂x∂y=∂2u∂y∂x Solution: We have u=excosy…

Q: If r(t) = (VE – 1, ln(10 – t), sin(2t)) then the domain of r is

A: