Consider the differntial equation dy/dx= (y-1)^2 cos(πx)
I did everything, but don't get this one part of the problem..
b) There is a horizontal line with equation y=c that satisfies this differential equation. Find the value of c.
A horizontal line $\displaystyle y(x)=c$ satisfies $\displaystyle \frac{dy}{dx}=0$. If $\displaystyle c$ is such that $\displaystyle y(x)=c$ satisfies the equation, then we must have $\displaystyle 0=(c-1)^2 \cos(\pi x)$ for every $\displaystyle x$. This implies $\displaystyle c=1$. Conversely, $\displaystyle y(x)=1$ is a solution.