Answer:
Step-by-step explanation:
we know that
A line parallel to the x-axis is a horizontal line
The equation of a horizontal line is equal to the y-coordinate of the point that passes through it
In this problem the line passes through the point (6,-6)
so
The y-coordinate is -6
therefore
The equation of the line is
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The question is:
Check whether the function:
y = [cos(2x)]/x
is a solution of
xy' + y = -2sin(2x)
with the initial condition y(π/4) = 0
Answer:
To check if the function y = [cos(2x)]/x is a solution of the differential equation xy' + y = -2sin(2x), we need to substitute the value of y and the value of the derivative of y on the left hand side of the differential equation and see if we obtain the right hand side of the equation.
Let us do that.
y = [cos(2x)]/x
y' = (-1/x²) [cos(2x)] - (2/x) [sin(2x)]
Now,
xy' + y = x{(-1/x²) [cos(2x)] - (2/x) [sin(2x)]} + ([cos(2x)]/x
= (-1/x)cos(2x) - 2sin(2x) + (1/x)cos(2x)
= -2sin(2x)
Which is the right hand side of the differential equation.
Hence, y is a solution to the differential equation.
Step-by-step explanation:
=20x14x;14x2x0;8x17;3x0;5x0;5y
=280x28x13;84x0;25y
=7840x3;46y
=27 126;4y