The function y = C/x2 + 4 is the general solution of The function y = C1cos(3x)

Question

The function y = C/x2 + 4 is the general solution of The function y = C1cos(3x) + C2sin(3x) is the general solution of The function y = C1e - 3x + c2e - 2x is the general solution of Give the differential equation that has y2 = Cx + 3 as its general solution. Give the differential equation that has y = C1sin(5x + C2) as its general solution. Give the differential equation that has y = C1 e - 4x + C2xe - 4x as its general solution. Given y = Ce6x is a general solution of the differential equation y'-6y = 0 Find a solution to the initial value problem Given y = C1e3x + C2e - 2x is the general solution of the differential equation y " -y ' -6 y = 0 Find a solution to the initial value problem [y " - y' 6y = 0, y(0) = 2, y' (0) = 5]

Explanation / Answer

7)

y = C/x^2 + 4

y' = -2C/x^3

y'' = 6C/x^4

so option B

8)

y = C1cos3x + c2sin3x

y' = -3C1sin3x + 3C2 cos3x

y'' = -9 C1cos3x -9C2 sin3x

so option C

9)

option C

10 )

none of the above

11)

none of the above

12)

option D

13)

y = 4e^6x

option f

14)

option b

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