(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[itex] \frac{dy}{dx} = y \sqrt{x} [/itex], f(9) = 5

3. 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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# Homework Help: Separable First Order Differential Equation

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