Use Superposition approach to find the genral solution of the following equation: у" — 2у' + 3у - -6 сos 3x + 6sin 3x

Q: 2. (a) Show that the points (-2x, 5x), (0, 4x), (6x, x) are collinear.

A: Given that: (-2x, 5x), (0, 4x) , (6x, x)

Q: Use De Moivre's theorem to find the following: 4 i. [1+ v3i]" -3 ii. [-1+ v3 i]

A: Given that: i. [1+3i]4 ii. [-1+3i]-3

Q: Given that the vectors X1 = () e- -2t ,X1 = (C)e-6t are solutions of a system x' = AX, do they form…

A:

Q: Use Cramer's rule to fins a solution: 3x-2y=4 6x-4y=0

A: Cramer’s rule:

Q: Find all solutions of cos2x + cosx = 0. + na, 3 + na, nK, wherenis an integer + 2nn, where n is an…

A: Simplification

Q: The formula in cell B1 is =A$2. auto fill is used by dragging B1's auto fill box across to c1,D1 and…

A: Enter A$2 in cell B1. Then Autofill is used by dragging B1's autofill box across to C1, D1, and E1,…

Q: Find the best approximation to u = (3,-7, 2, 3) as a linear combination = (2,-1,-3. 1) and =…

A:

Q: Find mZU. U /3 V m2U = %3D Submit

A: tan x = perpendicular / base

Q: Convert the differentral equatim into e S and Save nhe System: (20-70-4y)%3D0

A:

Q: make outbound 3B the corner achieve True false

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Verify the points (1,5) ,(2,3) and (-2,-1) are collinear or not

A:

Q: Find a non zero unit vecor î that is orthogonal to u1= (1,2,1) and Uz= (2,5,4) in R³.

A: The given vectors are u1=(1,2,1) and u2=(2,5,4) in R3

Q: Solve using Cramer's rule. 2x+8y = 11 4x+6y = 3 %3D %3D

A:

Q: The equation +y= 9 in 3-space is cylinder Select one TrueO FalseO

A:

Q: What is the sum of the coordinates at which the diagonals of ABCD intersect?

A: From the given figure, The equation of the diagonals can be written as :

Q: Use the equations aF OF az ax az ay and ax OF ду OF az az az az and ax to find ду 5yz + 8x In(y) = =…

A: F=5yz+8xln(y)-z2∂F∂x=8ln(y), ∂F∂y=5z+8xy, ∂F∂z=5y-2z∂z∂x=8ln(y)5y-2z, ∂z∂y=5z+8xy5y-2z=5yz+8x5y2-2zy

Q: Save the following Sef of Lincay equations using over relaxoation 10X, +X2 + X3 12 X, + 10X2 + X3 =…

A: Rewrite the given system of equations, to find x1, x2 and x3. Multiply each right hand side…

Q: baphress -4i in esponenial form reio the Qunge OLOC2TI in

A:

Q: Suppose that a parametrization for the solution set to the equation Ax = b is 3 + x2 + x3 8. -7…

A:

Q: Graph the image of rectangle CDEF after a rotation 180° counterclockwise around the origin. 10 4 2…

A: If we rotate 180 degree about origin the sign of the coordinates will reversed

Q: Express the following in Cartesian form

A: As,  cos 300o= 12 and sin 300o= -32. Now, put the values and simplify.

Q: A fence is to enclose a rectangular possible from with area of 400 square meters if P(x) is the…

A:

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A:

Q: Let z2T3-L p=S+Si O fird all the complex mumbers %3D guien by hza

A:

Q: Calculate the value of 1n(-V5 – V5i )

A:

Q: Find the four roots of z=1- jV3 (polar form only)

A: We need to find the four roots of : z=1-j3

Q: Find mZB. 141° 72° B 47° mZB %3D Submit

A:

Q: Show that the following gu are harmonic and find its conjugate U = 3x²³y + 2x² - y²³-2y²

A:

Q: Find a non zero unit vecor û that is orthogonal to u1= (1,2,1) and Uz= (2,5,4) in R³.

A: Cross product of two vector is perpendicular to both vectors.

Q: 7) If A = xz³i – 2x²yzj + 2yz*k, find VxA at the point (1,-1,1).

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: A particle start from the point (4,4) and it's coordinates change by the increment AY=5 and AX= -8…

A:

Q: Find the angle between the vectors (7, -6) and (7, 3). Carry your intermediate computations to at…

A:

Q: The formula in cell C2 is = A$2. Auto fill is used by dragging C2's auto fill box across to D2, E2,…

A:

Q: Find the resolvent kernel and Solut of ya) = I+5(1-3x+).y(t).d by Alternative procedure

A: Given Integral equation is y(x)=1+∫01(1-3xt)y(t)dt               (1) The general form of integral…

Q: What is the image of (-1, -4) after a reflection over the line y = -x?

A: Topic = Coordinate geometry   when a point is reflected across the line y = -x, the x-coordinates…

Q: To avoid collisions with invasive species of aliens, new imperial regulations allow only positive…

A:

Q: Find the angle between the vectors (-8, –7) and (-6, 4). Carry your intermediate computations to at…

A:

Q: Compute the order of each element in the Quaternions, Q8. Show your work.

A:

Q: Use DeMoivre's Theorem to find the following. Write your answer in standard form. V2 cis- 20 O…

A: Given (√2cos(9π/20))5

Q: Solve (y(1+1) + coxy) dan + [n+lope-nsmy] =

A: 25. The given differential equation is                                     y1+1x+cos ydx+x+log x-x…

Q: Compute Cixj)xk and un h Find patro of he pMane gog ingi (-i, novmetit tj 4K

A: The equation of the plane passing through the given point and perpendicular(normal) to the given…

Q: What is the image of (4,-1)(4,−1) after a reflection over the line y=xy=x?

A: Reflection over y=x means:  (x,y)→(y,x)  We need to find reflection of (4,-1) over y=x line .

Q: Use Powerseries to Solve the followwingdifferential .equations

A:

Q: Describe the tronsformaton that must be performed, On the of y=&5)*-3 gaph of y= xh to Obtuin the…

A:

Q: Graph the image of rectangle TUVW after a rotation 180° counterclockwise around the origin. 101" V T…

A: Topic = Geometry

Q: Show a complete soluton 2 3 CO-10y 10sin x

A: Given:

Q: Find the angle between the vectors (9, -5) and (9, 2). Carry your intermediate computations to at…

A:

Q: Find x so that (-2, 3), (x, 6), and (8, 8) are collinear.

A: Colinear:  For (-2,3),(x,6),(8,8) are colinear. -231x61881=0

Q: Three runners start at the same location and, at the same time, start running in different…

A:

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.