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This question is designed to be answered without a calculator.
The solution of dy/dx = (2sqrt(y))/x passing through the point (-1,4) is y =
1. ln^2|x|+2
2. ln^2|x|+4
3. (ln^2|x|+2)^2
4. (ln^2|x|+4)^2

PLS HELP This question is designed to be answered without a calculator. The solution-example-1
User Amit Aviv
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1 Answer

11 votes

The given differential equation is separable:


\displaystyle (dy)/(dx) = \frac{2\sqrt y}x \implies \frac1{\sqrt y} \, dy = \frac2x \, dx

Integrate both sides:


\displaystyle \int y^(-1/2) \, dy = \int \frac2x \, dx


2y^(1/2) = 2\ln|x| + C


2\sqrt y = 2 \ln|x| + C

Given that y(-1) = 4, we find


2\sqrt4 = 2\ln|-1| + C \implies C = 4 - 2\ln(1) = 4

Then


2\sqrt y = 2 \ln|x| + 4

Solve for y :


\sqrt y = \ln|x| + 2


\left(\sqrt y\right)^2 = \left(\ln|x| + 2\right)^2


\boxed + 2\right)^2

User Aerojun
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