Question

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?)

Answer 1

collect all the terms that have y on one side, and x on the other, and then integrate:
\[\frac{1}{y} dy = \frac{1}{2\sqrt{x}} dx\]
\[\ln{y} = \sqrt{x} + C\]

Answer 2

exponentiate both sides
\[y = e^{\sqrt{x} + C} = Ce^{\sqrt{x}}\]

Answer 3

plug in initial points to solve for C:
1 = Ce^2
C = 1/e^2

plug C back into general solution:
\[y = \frac{1}{e^2}e^{\sqrt{x}}\]