Question 1143288
<pre>
{{{(dy)/(dx)=x*sqrt(1-y^2)}}}

Multiply both sides by dx

{{{dy=x*sqrt(1-y^2)dx}}}

Divide both sides by {{{sqrt(1-y^2)}}}

{{{(dy)/sqrt(1-y^2)=x*dx}}}

{{{int( (dy)/sqrt(1-y^2) )}}}{{{""=""}}}{{{int(x*dx)}}}

Use the formula: {{{int((du)/sqrt(a^2-u^2))}}}{{{""=""}}}{{{arcsin(u/a)+C}}}

{{{arcsin(y/1)}}}{{{""=""}}}{{{x^2/2^""+C}}}

{{{arcsin(y)}}}{{{""=""}}}{{{x^2/2^""+C}}}

Take the sine of both sides:

{{{y}}}{{{""=""}}}{{{sin(x^2/2^""+C)}}}

Edwin</pre>