Which of the following is a general solution to the followin x²y"+xy'+ (x²– 1)y=0 y=c,(x) +cY_,(x) O y=c,J,lx)+cJ,(-x) y=c,J,(x) +c_r,(x) O y=c,(x)+cJ_(*)

Q: Cansider h(x)= Ilx? -6x = l|x? calculate Ha) 6 .x T1 3 (22r – 6) A) In(3)- 11 (22.r – 6)3** - (11z²…

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Q: Prove that Ją (2) = =- J¼ (2) – J_4 (=)

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Q: Find L[et tsin(2t) - e-2t+3 +e-2t cos 3t]

A: BY USING THE LAPLACE TRANSFORMATION RULES  WE GET OPTION (D) IS CORRECT OPTION.

Q: Given fex) End (f-')'(5) 2X

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Q: (4) VL1, L2 ((L1 UL2)* = L₁* U L₂¹).

A: This is always True

Q: Given y = (x + 1)(x + 2)² Find: y O (z + 2)(3x – 4) O (2 – x)(3x – 4) - O (x – 2)(3x + 4) O (2 +…

A: Apply the product rule of differentiation f·g'=f'·g+f·g' to find the derivative of the given…

Q: y = C1e¬ª + C2e¯2# + x y" + 3y – 2x + 2y – 3 = 0 y" – 3y – 2x – 2y+ 3 = 0 - - Option 1 Option 3 y" –…

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Q: 2) y¨+y=1+x+x'

A: To find the general solution of  y''+y=1+x+x²

Q: 5) U₂ = 5 Uxx t U(0,€) = 2 U(3,4)=-1 U(x,0) = -x

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Q: The top and bottom margms Op a poster are are 8 cm and Hhe Side mary Ms'are each 6 cm if Hhe ae a of…

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Q: If x + y +z = 12 & x² + y? + z? = 96 & !+!+!= 36 then value ху Z of x + y³ + z³ is

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Q: (*) Y(z) 16z (2²+1)(4z-1)(2z-1) Now partial fraction is 16z 112 96z 16 (z²+1)(4z-1)(2z-1) 85(+1)…

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Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: 9. z + j/2

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Q: Ay A'y A'y X y 1-1 -1 -2 2 1 3 -1 3 is given by x² – 4x +2 x2 O x? +2 x2 + 4x +2 4,

A: See the attachment

Q: (1) VL1, L2 (L1 L2 iff L₁* = L₂"). True

A: False. The statement is not true in general.

Q: F U(X,Y) IS THE SOLUTION OF THE CAUCHY PROBLEM                     XU\index{X}+U\index{Y}=1…

A: xux+uy=1ux,0=-x2, x>0

Q: Vr+2+Vx-2 If a = prove that a -ax +1=0 Vx+2-Vx-2

A: To prove , we need to simplify the left hand side of the equation till it becomes 0. To do this…

Q: X~N(0,1), Y~N(1,4), X and Y are independent of each other, then 2X+3Y+3 ~ ( )

A: X~N(0,1) and Y~N(1,4)

Q: 9. Find the general solution of (D² – 2D+ 1)y= 6e*. A) y= (c, +c,x)e* + 3e™* B) y= (c, +c,x+ 3x² )e*…

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Q: Q6 : find 1) j(1 – jv3)(v8 +j) 2) (1+j)(1– j/3)² 3) cos-1(2)

A: (1) j(1-j3)(8+j) Use the property (a+b)(c+d)=ac+ad+bc+bd in the expression (1-j3)(8+j) and…

Q: Let f(x) f'(x) find the values of A = B = C= D = 1 3x4+x3 + x -5 x3 -5.5 - X + 13.2 = (2AB-1 Given…

A: The given function is: f(x)=3x4+x13+x-5x3-x-5.5+13.2

Q: 1) xy' x+y

A: As per bartleby guidelines only 1 question can be answered please upload each question separately…

Q: 1. f(x) = x² – 4x + 1 at point (0,1) 2. f(x) = x³ + 2 at point (1,3) 3. f(x) = 2x* + 3x³ – 2x + 7 at…

A: Given : The functions and the points.

Q: 35) y+ y, =-5cos(2t), y+y, = 5cos(2t), y;(0) = y{(0) =1, y,(0) =-1, y,(0) = 1.

A: The solution is given as

Q: Əz x²y + 7y²z + xz² = 9 ax'

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Q: X= 2 etsin(2t) etcos(2t)

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Q: 7- Differentiate K(x)=(Vx)(5x²+1)³

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Q: Complete the sentence below. Iff is a one-to-one function and f(3) = 6, then f(6) = If f is a…

A: One one functions

Q: 2 1) (-2xy) dx + ( Sing-x²) dy

A: As per our company guidelines we are supposed to answer only the first question. Kindly re post the…

Q: What is r' (x) when r(x) = In ? Select the correct answer below: O Pu) = - Sr+1 O rw = - Sr+1 x) = !…

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Q: 09. C-1 28-1 $²-8-6 (e³ (t-1) + e-2(t-1)) u₁ (t) C. (e-3(t-1) + e²(t-1)) u, (t) <-8 e 0} (1) A. (t)…

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Q: If V=R\power{3}, and W\index{1} is the xy plane and  let W\index{2} is yz-plane:…

A: Let (a,b,c) be any element of R3, then (a,b,c)=(x,y,0)+(0,y,z)=(x,2y,z) ⇒a=x, b=2y, c=z ⇒a,b,c∈R ⇒…

Q: Let x, y ER" and let a E R. Each of the following is true except: (b)-(ax) = (-a)x. (a) a (x + y) =…

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