Show that the equation dy + 2k possesses solutions of the form E c, e cos (a,x+&,) cos (w,t+ 8,) where c, , o, , Er , 8, are constants and w, 2 22 = a c² -.

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Q: 1.5 (3-x Q1) Evaluate the integral * dy dx using polar coordinate

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Q: in Let an n> 1. In(2" + 1)' 1. Determine if the sequence {an}n=1 is convergent or divergent. 2.…

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Q: 2. Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the matrix.

A: We have to find the characteristics equation eigen values and eigenspaces of given matrix.

Q: Q2) Solve the D.E dy + (xy – xy²)dx = 0

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Q: Find the eigenvalues and eigenvectors of the matrix A 0 -3 0 -8 and and d3 = b3 = || ||

A: Given matrix is A = -3010-30-40-8

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Q: salvepE tany= Sin(2 +y) +Sin(x-y) (ans. secy= C-2 Casx)

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Q: Solve: (dy/dx) = [(5y - 2x) /(4x – y )] %3D

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Q: Solve: (dy/dx)? + (y- 1– (x/y)) dy/dx <- x/y(y– 1 ) = 0

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4-x from above inside x = y? ,x = 4.

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Q: a2 b2 C2 If Aj = [di ei fi] A2 = [d2 e2 2] real numbers, show that: 9. (A, +A,) + Az = A, + (A, +A3)

A: # As per the guidelines we are entitled to solve one question at  a time ,please resubmit the other…

Q: Solve: (dy/dx)? + (y– 1– (x/y)) dy/dx – x/y(y-1) = 0 |

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Q: Q2) Solve the D.E dy + (xy – xy²)dx = 0

A: The solution is given as

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Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: How %3D ne

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Q: QI) Evaluate the integral dy dx using polar coordinate

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