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tinopham
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Homework Statement
[itex] \frac{dy}{dx} = y \sqrt{x} [/itex], f(9) = 5
The Attempt at a Solution
[itex] \int dy/y = \int \sqrt{x} dx [/itex]
[itex] ln |y| = \frac{2}{3} x^\frac{3}{2} + c [/itex]
[itex] y = e^{\frac{2}{3}x^\frac{3}{2}} + C [/itex]
[itex] y = Ce^{\frac{2}{3}x^\frac{3}{2}} [/itex]
[itex] 5 = Ce^{\frac{2}{3}9^\frac{3}{2}} [/itex]
[itex] 5 = Ce^{18} [/itex]
[itex] C = \frac{5}{e^{18}} [/itex]
Thus,[itex] y = \frac{5}{e^{18}} e^{\frac{2}{3}x^\frac{3}{2}} [/itex]
[itex] y = 5e^{-18} e^{\frac{2}{3}x^\frac{3}{2}} [/itex]
[itex] y = 5 e^{\frac{2}{3}x^\frac{3}{2}-18} [/itex]
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