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**Unformatted text preview: **the line p = 1 . 5 . Indeed, the constant Function p ( t ) â‰¡ 1 . 5 is a solution to the given logistic equation, and the uniqueness part oF Theorem 1, page 12, prevents intersections oF solution curves. 6. (a) The slope oF a solution to the diÂ²erential equation dy/dx = x + sin y is given by dy/dx . ThereFore the slope at (1 , Ï€/ 2) is equal to dy dx = 1 + sin Ï€ 2 = 2 . (b) The solution curve is increasing iF the slope oF the curve is greater than zero. Â±rom part (a) we know the slope to be x + sin y . The Function sin y has values ranging From âˆ’ 1 to 1; thereFore iF x is greater than 1 then the slope will always have a value greater than zero. This tells us that the solution curve is increasing. (c) The second derivative oF every solution can be determined by fnding the derivative oF 11...

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