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WARRIOR [948]
3 years ago
10

Passes through (-1, -5) and (2, 6)

Mathematics
1 answer:
patriot [66]3 years ago
3 0

Answer:

y = \frac{11}{3}x + -\frac{4}{3}

Step-by-step explanation:

y = mx + b\\m = \frac{-5 - 6}{-1 - 2} = \frac{-11}{-3} = \frac{11}{3} \\\\y = \frac{11}{3}x + b\\6 =  \frac{11}{3}(2) + b\\6 = \frac{22}{3} + b \\6 - \frac{22}{3} = b \\b = -\frac{4}{3}\\\\y = \frac{11}{3}x + -\frac{4}{3}

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Answer:

y = 2cos5x-9/5sin5x

Step-by-step explanation:

Given the solution to the differential equation y'' + 25y = 0 to be

y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.

According to the boundary condition y(0) = 2, it means when x = 0, y = 2

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If y'(π) = 9, this means when x = π, y'(x) = 9

On substituting;

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9 = 0-5c2

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Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation

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y = 2cos5x-9/5sin5x

The final expression gives the required solution to the differential equation.

3 0
3 years ago
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