(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Im having trouble with "initial value" problems. I cant seem to grasp the "way" around it. any help is greatly appreciated.

[tex]\sqrt{}1-y^2[/tex] dx - [tex]\sqrt{}1-x^2[/tex] dy = 0

y(0) = sqr(3) / 2

2. Relevant equations

solve by separation of variables and inital value.

3. The attempt at a solution

rearranging

i get dy / [tex]\sqrt{}1-y^2[/tex] = dx / [tex]\sqrt{}1-x^2[/tex]

integrating

arcsin(y) = arcsin(x) + c

y = sin (arcsin (x) + c))

y (o) = sqr3/2

c = pi/3

therefore y = sin(arcsin x + pi/3)

the back of the book says:

y=.5x + sqr(3)/2 ([tex]\sqrt{}1-x^2[/tex]

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i was reading the book but theres only 1 example about initial value problems.

so If anyone can give me "tips" on how to solve this problems that'd be great

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# Homework Help: Differential Equations

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