Solve the following differential equation using both the method of trial functions and the method of variation of parameters d²y dx2 dy 6- dx 7y = e²x with y(0) = 3 and y'(0) = 2.

Q: 28. Show that tan z = sin(2x) + i sinh(2y) cos(2x) + cosh (2y)

A: We can show the given identity.

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Q: Question 5. Let A = {0,1} and B = {1,2}. Find: (a) (A x B) U (B x B) (b) P(A) \ P(B).

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A: The given differential equation is

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A: I have provided detailed proof for each question in the Explanation section.Explanation:Let's go…

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A: Given the bilinear form  defined by.The ordered basis of R2 is .

Q: Need help with these two Intro to Elementary Number Theory Homework problems.

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Q: Plz explain properly.

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Q: Needs Complete solution with 100 % accuracy.

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Q: (c) AB (d) |AB|

A: |A| = -15, |B| = 52, |AB| = -780Explanation:

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A: We will find the integral approximations T8 and M8.

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Q: Approximate the following integrals using the Simpson's rule S" 3/(x2-17) dx where b = 0.356.

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Q: Form a differential equation by eliminating the arbitrary constant a and b from the equation y = ax²…

A: Differential equation will be, y=xdxdy​−2x2​dx2d2y​  Explanation:

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT SOLVE BY BERNOULLI OR INTEGRATING FACTO

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A: LetWe have to evaluate the above integral.

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Q: Problem #6: Consider the same system as given in the previous problem: S3xu² + 2y v4 = 5 4xy(u² -…

A: a) The system of the equation is :The aim is to find a) b)

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Q: I have: P(E)=25/100      P(F)=50/100    P(F|E)=17/25      P(E|F)=17/50 I don't know if E and F are…

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