Linear Differential Equations
Determine whether the given relation is an implicit solution to the given equation.
sin(y)+xy-x^3=2-----relation
y''=(6xy'+((y')^3)sin(y)-2(y')^2)/((3x^2)-y)-----equation
The book says yes it is a solution but for some reason I am not getting it. You have to use implicit differentiation(duh).
What I did, which should be the right steps, is get the second derivative and solve for it(go from y-y'-y'' and isolate y''). Maybe I'm missing something.
This is what I got:
y''=(2y'sin(y)-2y'+6x)/(cos(y)+x)