1. ## Slope field question

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.

2. Originally Posted by elpermic
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 $y(x)=c$ satisfies $\frac{dy}{dx}=0$. If $c$ is such that $y(x)=c$ satisfies the equation, then we must have $0=(c-1)^2 \cos(\pi x)$ for every $x$. This implies $c=1$. Conversely, $y(x)=1$ is a solution.