If x, x is a basis of solutions of r'y" + ary'+ by = 0, %3D then a = (A) -2 (B) 2 (C) -3 (D) 3 (E) None

Q: Convert y " – 2y " +y=sin(4 t) into a system of first-order equations. a) O [* =*; *;=x X=- 2x,+…

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Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given…

A: Introduction: Row reduction, also known as Gaussian Elimination, is the second technique for…

Q: 1. The vector X = k is a solution of x - (: -)x-G) 8, X' 2 for k = Enter only the value of k.

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Q: a C:) = C; )C) + (;) d %3D dt What is the general solution of the above inhomogeneous state space…

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Q: If r(t) = = cos(-3t)i + sin(−3t)j – 10tk compute r' (t)= i+ i+ (cos (-3t))/3 and fr(t) dt= (-sin…

A: r(t)=cos(-3t) i+sin(-3t) k-10tk

Q: 7. Use Romberg method to calculate 2dx.

A: Romberg Integration is given as :-I=∫abf(x)dx=Rn k+O((b−a2n)2k+2)R0 0R1 0R1 1⋯⋯⋱Rn−1 0Rn−1 1⋯Rn−1…

Q: A researcher wants to analyze the effect of a variable x on another variable y using observations…

A: Given the estimated model for the variables x and y as I yi=β1+β2xi+ei II yi=β1+γ1ri+β2xi+γ1xi…

Q: 9. Consider the column vectors u and v in R" cos(0) cos(20) sin(0) sin(20) u = v = cos(n®). sin(nº).…

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Q: 2y" + 3y' - 2y = 3xez* - 2sinnx (Use Method of Undetermined Coefficients (MUC))

A: The given differential equation 2y''+3y'-2y=3xe12x-2sinπx. We have to find the general solution…

Q: Write the system y1 = -y1+2 cos(r)y3 + e 2 = xy1 - 10y2 + e" y3 +20 sin(x) Y3 = e2" y2 – a²y3 %3D…

A: The matrix form of given system of differential equations as follows

Q: 2) z(x, y) = (x² + 5y)³ (3y + 2x)

A: Let's find dz/dx and dz/dy.

Q: 2 [11]₁v=₁-1²] W u Compute: u.v= u. W = w u · (v + w) = u.v+u. W =

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Q: 6. (E) Prove that there are no solutions to the equation 2x² + 5y² = 32² in positive integers (x, y,…

A: Given equation is    2x2+5y2=3z2  ------ (1)  Let's suppose that we have a solution x,y,z where…

Q: 23 at the poles (1+i)//2 and (-1+i)//2. Find the residues of 24 +1

A: Let f(z)=z3z4+1 and it has simple poles at 1+i2  and -1+i2. The residue of any f(z) at simple pole…

Q: 20. е -3.1х cos 2.1x, e -3.1х sin 2.1x

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Q: A matrix function A and a vector function b are given. Write the system of equations corresponding…

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Q: (2) Sketch the direction field associated to the system I'=x²-y-3, y = y + x² - 5. Include the…

A: sketch the direction field associated to the system    x' = x 2 - y - 3 y' = y + x 2 - 5   include…

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: y"+y' + (a) -5 x-b = 0, Xo = 2 is 5. (b)-3 (c)-2 d)-8 Q7) L(y") = a) s²L(y(x)) + sy(0) - y'(0) c)…

A: We have given the answer in the next step. Hope you understand that

Q: QUESTION 4 a) Let (27¹) Calculate the products A. B and B. A, and the determinant det (A). b)…

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Q: 5 6 0 Compute the quadratic form x'Ax for A = 6 3 1 and each of the following vectors. 0 14 X1 1/ 3…

A: Transpose of each column vector is a row vector. We do simple matrix multiplication to compute the…

Q: Let X'Y' -system be obtained from XY –system by a rotation through 45°. Describe the equation 2x2 +…

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Q: di ) = (} a G) = (3 )G) + (G) What is the general solution of the above inhomogeneous state space…

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Q: Q2)A) If U (x,y)%3DXY-sin n is a function and x,y are function of r,9 defined as follow x =r cos 9 y…

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Q: (2) Consider the following vector ODE 2 1 1 Y': × - (D) - - () 0 2 -1 Y + 0 0 0 -1 (a) Convert it…

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Q: Example 4: Solve y" + 7y' + 10y = 2x + 3e*. y" – 3y' - 4y = 2x2 - 3. iii) y" + 2y'-3y 7x-3x. iv) y"…

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Q: If {1, e²x, xe²*} is a basis of solutions of y"" + ay" +by' + cy = 0, b= 2 (b) -2 -4 (d) 4 (e) 0

A: We can start by substituting the basis functions into the differential equation and solving for a,…

Q: Suppose A is not diagonalizable. If the characteristic equation of A is: -λ +2^² - 2³ = 0 then dim…

A: Given :-  A is not diagonalizable. And Characterstics equation.  Topic :- Matrix.