## 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?)

1. anonymous

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

2. anonymous

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

3. anonymous

plug in initial points to solve for C: 1 = Ce^2 C = 1/e^2 plug C back into general solution: $y = \frac{1}{e^2}e^{\sqrt{x}}$