Question

E) Let y = g(x) be the particular solution to the differential equation dy/dx= 3sin(pix)/2y with initial condition

g(1/2)=3. Then g(x)= sqare root of a+bcos(pix) where a and b areconstants. Find a

Answer 1

9

Explanation:

You want the value of the constant 'a' in the solution y=√(a+b·cos(πx)) to the differential equation y'=3sin(πx)/(2y) with initial condition y(1/2) = 3.

Initial condition

Substitute the initial condition into the equation for y:

y = 3 . . . . when x = 1/2

y = √(a +b·cos(πx))

3 = √(a +b·cos(π/2)) = √a

3² = a = 9

The value of a is 9.

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Additional comment

The value of 'b' is -3/π.

It can be found by putting the equation for y in the original differential equation, and solving for b.