when do we have to look for a constant solution to the differential equation?
Example: Solve the initial value problem $\frac{dy}{dx} = \frac{2}{\sin y}$ with the condition $y(0)=0$.
The first step in the worked solution is as follows: Noting that $\frac{1}{\sin y} ≠ 0$ for any $y$, we see there are no constant solutions.
My question is: do we always have to look for constant solutions when solving any differential equations? and what is the significance of the constant solution? thank you
Best Answer
The significance of constant solutions - is the fact, they are constant. In order to find them, you need only to find the zeros of the right hand side, i.e. they are - in general case - easy to find.