Question

help with implicit functions...

Answer 1

show that \[xy^3-xy^3sinx=1\]
is an implicit solution to \[y'=\frac{ (xcosx+sinx-1)y }{ 3(x-xsinx) }\]
on the interval (0,pi/2)

Answer 2

o,pi/2 interval suggests the 1st quadrant. where nothing specific is required no problems or intricacies with signs.
rearrangement of equation: \[xy^3 (1-sinx) = 1\]

Answer 3

\[y^3 (1-sinx) = 1/x;
differentiating both the sides we get;
3y^2 (1-sinx) dy/dx = -1/x^2\]