Find the solution of the given initial value problem in explicit form
y'=(1-2x)/y ; y(1)=-2

Question

Find the solution of the given initial value problem in explicit form
y'=(1-2x)/y ; y(1)=-2

loser66 · Answer

$$\frac{dy}{dx}y =1-2x\ydy=(1-2x)dx$$
integral both sides I got the answer is y =+-sqrt(2x-2x^2 +c
solve for c , I have c=4
so the answer should be +- sqrt(2x+2x^2+4
However, the answer in book reject positive answer, why?

phi · Answer

are you saying the answer is 
$$ y= \pm \sqrt{2x - 2x^2 +4} $$

at x=0  you would get
$$  y = \pm\sqrt{4} = \pm 2$$
based on y(1)= -2,  you can only use the - sign solution

dan815 · Answer

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