Question 10 dz will be equal to ax Given the equation f(x,y,z)= x3+y3 +z3 + 6xyz- 1, then OA x2-2yz OB. 2(x2 +2yz) OC. x2 +2yz OD.None of the choices in this list. z2 +2xy z2 +2xy 22 +2xy

Q: QUESTION 1 (a) Obtain the general solution of the equation = 2xy. (3 Marks) (b) Find the solution of…

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Q: Show that the equation 2²2 2 2²y Əy +2k c². əx² de ² Ət possesses solutions of the form 0 - kt Σ Cre…

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Q: Question 2: Consider U(x, y) = xy. Verify that (1, 1) and (2, 1/2) give the same utility level. Now…

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Q: 2. f(2y+3)y+2 dy

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Q: Question 16 In obtaining the solution of Y 2dy – (x'+y')dr=0 when y ()=0 what is the value of C? A B…

A: Differential equation

Q: (b) D₂f = 2 cos(xy + 2z) Dzzf = -4 sin(xy + 2z) Dzzyf = -4x cos(xy + 2z)

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Q: 8. If fx) = cos (2x), findf '(). TC %3D a. b. c. 1 d. -1

A: The given function is f(x) = cos2(2x) Differentiate with respect to x using chain rule…

Q: Question # 2 (a): Find and of the following ax (a) z = e*Ysin5y² (b) z = Vx+y

A: ∂z∂x means partial derivative of z with respect to x considering y as a constant ∂z∂y means partial…

Q: Question 3 Give the form of a particular solution of y"" + 2y" +9y' +18y = 3e-4 + sin(3x) - 3x.…

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Q: Question 3 Solve y"+7y'-8y=0;x=0,y=0,y'=1 y at t=1 O 0.302 O 0.393 O 0.332 O 0.0338

A: To find out the value of y at t=1.

Q: C. 2よx dり CSCO ウこ0)ウこ6 V coso.vdvdo CSCO ウニズ vcosodrde CSCO tano=2 Cosede tano=1 Tん O= tan'(1) %3D…

A: Solution is given below:

Q: Given that y1(x) = cos x is a solution to the ODE: (sin r)y" – 2(cos r)y' – (sin æ)y = 0 Then the…

A: The given differential equation is: (sin x) y''-(2 cos x) y'-(sin x) y=0Therefore:y''-(2 cot x)…

Q: 12. (D3 - 6D2 + 9D - 54)y = 0 a. y = Ce + C2 cos 3x + C3 sin 3x %3D b. y = Cex+ Cz cos 4x + C3 sin…

A: follow next step

Q: Uk+2(x) – 3k. dx duk+1(x) d²uk + 2k(k – 1) 0, (8.295) dx2 has, in the x variable, the structure of a…

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Q: Question 7 Find the solution. (D² - 2D - 3)y = 0; when x = 0, y = 0, y'= 4 - 3x – e 2x A y = - „3x…

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Q: a) z=cos² (3 xy) onde x=p+eº ey=p²-2e³8 b) z=4x³y onde x=3p²+0² e y=p²-40²

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Q: 1. The loop of y = x '(4 - X) 2. y = 6x – x², y = x²– 2x 3. у %3D2х y? + 4x – 8 = 0 4. An arch of y…

A: As per the guidelines we can solve 1 problem only

Q: Question 9 x² – 4 Evaluate: V A =Vx² - 4 – 2 sec-+ c =V x2 – 4 + sec¯ + C = 2/x? – 4 + sec + C D x2…

A: The integration of the integral is sqrt(x2-4)/x.

Q: 5. The particular solution (when x = 1, y = 0) of cos y y e* + xe* +6^-4 dx +x e* - 4+ y dy 0 has…

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Q: The particular solution (when x = 1, y = 0) of %3D X 4 dx + x e* - 4+ y cosy |dy = 0 Уе + xе* + 6- -…

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Q: Question 28 F(x) = | " dt is equal to 65612 You Answered None of the given choices Correct Answer O…

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Q: 2. If y = -2u² + 3u + 6 and u = dy x²+5 ' a. Find using Leibniz notation. dx dy| b. Find dxx=2

A: The given functions are, y=-2u2+3u+6 and u=8x2+5 The required derivative is dydx. It is evident that…

Q: The general solution of (D²+2D+1)(D²+4)y=0 is A y=(C,+C,x)e+C,cos2x + C ,sin2r B) none of the given…

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Q: 6. A particul (a) z = Ae-2 cos a + Be-2* sin z + Ca -2x -2x (b) z = Ae cos a + Be 2 sin a+ Ca? (c) z…

A: As per our guidelines we need to solve only one question.please repost the remaining questions as…

Q: 1 All points of the equation (x + 2)y" + xy' + y = 0 are ordinary except O1 -2 and 0 O-2 and 1 None…

A: Correct ans is = - 2 and 1 Please find attachment for the details solution

Q: . Find the real coefficients a and b such that the function u = 4r +4r'y+ar y² -4ry+by is harmonic…

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Q: The equation (3xcos (3x) + sin(3x) – 3) dx + (2y + 5) dy = 0 is exact. Solve it. xsin (3x) + y + 5y…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Question 3 (c) dw z - w Find in terms of z and w in + 1. dz z+ w Solution

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Q: Question 3 Consider the IVP: y" + 9y = 40e* ; y(0) = 5, y'(0) = -2. Find the general solution. A)…

A: Laplace transferom, solution of the ordinary differential equations

Q: Chapter 4 1. If f(x, y)= 3x' sin y- y° cos. cos x- 2y n x - xIn y- 4xy , find- ôf ôf ô²ƒ ô²f a²f _…

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Q: 2 C, e-kt Show that the equation dy + 2k - possesses solutions of the form 00 cos (C, x+ E,) cos…

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Q: Consider the equation y' + 5y = 2. Show that the function o given by: %3D 2 $(x) is a solution,…

A: Given y'+5y=2 We have to find ∅x

Q: (-n/6, 3) (지2, 3) (z16. -3) (37/6. –-3) From the graph, write the equation in the form f (x) = A…

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Q: 1. [5an2f elan 28 sec² 2 Båß 3. e +1 2x e2x +2e* dx e* +1 4. |(30shm +ecoshm' 2.

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Q: QUESTION 13 For z = f(x,y) and x = s+t and y = 15S-15t If at a point (X0,Yo) we have Zx=12 and Z, =…

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Q: Question 5 of 8 Determine the particular solution: y"+y'+ 2y = 0, y(0) =0, y'(0) = 0 Select the…

A: We have to find out

Q: QUESTION 1 1 where r = x² + y² +z² , then xw, + yw, + zw̟ is: 1 А. 1 С. 1 D. В. r Show your working…

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Q: 1) Rewrite c(r) = 2+5z+2 I-3 in the form y= q(x) + He where r has degree less than b.

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: sketch the odd and even extensions for -3,3]. Use the substitutions : '= ye¯* s = x Q.3 to solve the…

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Q: Question 7 of 8 Determine the particular solution: y" - 2y'+y = 0, y(0) = 5,y'(0) =10 Select the…

A: Topic = Differential equation

Q: 2 C, e kt Show that the equation dy 2. + 2k possesses solutions of the form 00 E c, e " cos (a, x+…

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Q: Show that the equation + 2k dy =c². possesses solutions of the form 00 2 c, e " cos (a, x + &,) cos…

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Q: Show that the equation dy + 2k possesses solutions of the form 00 Σ C,e -kt cos (a, x + E) cos (w,t+…

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Q: Question 11 Find the solution, (D3+3D²+3D+1)y = 0 (A y = (c,+c,r+cx?)e= © y = c,e"+c,„xe -3«. Oy =…

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Q: Question 20. Solve simultaneously 5x + y = -1 and y = a? + + 4 Enter your pairs of solutions for (x,…

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Q: The equation (3acos (3a) + sin(3x)-3) dr + (2y + 5) dy = 0 is exact. Solve it. O zcos (3z) - 3x +y -…

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Q: Given: [(4x + 3)²D² - 12(4x + 3)D +64]y = 16[(4x + 3)² sec² (In 4x +31)], what special case is this?…

A: Given 4x+32Dx2-124x+3Dx+64]y=164x+32 sec2ln4x+3 what special case is this? (A) Cauchy-Euler Equation…

Q: Show that the substitution u = y' leads to a Bernoulli equation. Solve this equation.…

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Q: Question 3 of Assume w = fts, 6ts) and (x) = 4xy and (x)=2x Fid as when t = S = 1 A 50 1 B. 60 C. 52…

A: Consider the given information. w=fts2,6ts Now, find the function. ∂f∂xx,y=4xyfx,y=2x2y And,…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.