- #1
fiksx
- 77
- 1
Homework Statement
$$y'=-\frac{1}{10}y+(cos t)y^2$$
when doing substitute for ##z=\frac{1}{y}##
I understand this is ##z(t)=\frac{1}{y(t)}##
I know t is independent variable and y is dependent variable
but I want to know what is z role here, is it change the dependent variable?
when ##y(t)=\frac{1}{z(t)}##
then
I saw in book it is written ##y'=\frac{-z'}{z^2}##, is this means ##y(t)'=\frac{dz}{dy}\frac{dy}{dt}##?
is the relation is ##z(y(t))##? can someone explain the implicit differentiation in this expression? and what is dependent and independent variable here? thanks!
I understand how to finish this. but I want to know the intuition behind this. I always confuse when doing substitution, what is the dependent and independent variable, and to what variable I need to implicitly differentiate.
Homework Equations
The Attempt at a Solution
Last edited by a moderator: