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anonymous
 5 years ago
dy/dx = y/(2sqr(x)) and y = 1 when x = 4. solve. ( one question in my homework, can any one please show me how to work this?)
anonymous
 5 years ago
dy/dx = y/(2sqr(x)) and y = 1 when x = 4. solve. ( one question in my homework, can any one please show me how to work this?)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0collect all the terms that have y on one side, and x on the other, and then integrate: \[\frac{1}{y} dy = \frac{1}{2\sqrt{x}} dx\] \[\ln{y} = \sqrt{x} + C\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0exponentiate both sides \[y = e^{\sqrt{x} + C} = Ce^{\sqrt{x}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0plug in initial points to solve for C: 1 = Ce^2 C = 1/e^2 plug C back into general solution: \[y = \frac{1}{e^2}e^{\sqrt{x}}\]
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