Question

Find an explicit solution of the given initial-value problem.
sqrt(1-y^2)dx-sqrt(1-x^2)dy=0
when y(0)=1/2

Answer 1

i got to the part of y=sin(arcsin(x)+C)

Answer 2

plugging y0=1/2

Answer 3

gives 1/2=Sin(C)

Answer 4

how do i get the constant out by its self?

Answer 5

is it correct if i jus do arcsin on both sides

Answer 6

Assuming all your work is right so far, you can isolate C by taking the inverse sine of both sides. So what's \(\arcsin\dfrac{1}{2}\)?

Answer 7

pi/6

Answer 8

Right. And just to check: http://www.wolframalpha.com/input/?i=sqrt%281-y%5E2%29+dx-sqrt%281-x%5E2%29+dy%3D0%2C+y%280%29%3D1%2F2

Answer 9

so can i say my explicit solution is y=sin(arcsin(x)+(pi/6))

Answer 10

oh nice i totally forgot of wolframalpha today

Answer 11

Yeah, that's it

Answer 12

thx

Answer 13

yw