Find the solution of the given initial value problem 98y" +21y" + y = 0, y(0) = −8, y'(0) = −14, y'(0) = 0. On paper, sketch the graph of the solution. How does the solution behave as t→∞? y(t) = As t → ∞, y(t) —

Q: (c) A function y(t) is a solution of y' + ky = 0. Sup find: (i) k (ii) y(t)

A: It is differential equation problem

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Q: Solve: x" -x+ 5 y'=t y" - 4y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: Find the solution of y" – by' + 9y = 16 et with y(0) = 2 and y' (0) = 1.

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Q: (ii) 42?у" + у — 0. 4.x

A: Consider x=et and differentiate to obtain the expression of dtdx . x=ett=lnxdtdx=d dxlnx=1x Break…

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A: Solution:

Q: Determine 4sin(x); the value of the arbitrary constants y(x) = C₁e* + c₂e¯* + y(0) = 1, y'(0) = -1…

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Q: Find the solution of with y(0) = 7 and y'(0) = 6. y" + y − 2y = 54 et

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Q: (a) y" – 4y" + y' + 6y 0. (b) y" – y" + 2y' = 0.

A: General solution for the Homogeneous differential equations with constant coefficients

Q: Solve: x" -x+ 5 y'=t y" - 4 y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: (a) Find the local extreme values of the function f(x,y) = 2xy – x² – 2y² + 3x + 4. (b) Solve the…

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A: Given :

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Q: Find the solution of y' = (1 – 4x) y², y (0) = –1 in explicit form

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Q: Solve y"(t)- 2y' (t) + 5y(t) = H(t); y(0) = 0; y'(0) = 1; where H(t) = (t+2,0 ≤t <2 2t - 3,122

A: We have to solve by Laplace transform.