Consider the differential equation dy/dx = (y-1)^2 cos(Πx)

[gonzalo12345]

HW help!

Homework Statement

consider the differential equation dy/dx = (y-1)^2 cos(Πx)

a.There is a horizontal line with y =c that satisfies this equation. Find the value of c
b. Find the particular solution y =f(x) tot the differential equation with the initial condition f(1) = 0

Homework Equations

n/a

The Attempt at a Solution

I tried to do the problem, but I can't separate the y variables from the x, help!

 

[PingPong]

(a) What happens when you plug y=c to the differential equation? You should get just an equation depending on c (and x, but if you restrict x, you can divide it out).
(b) Try multiplying each side by dx/(y-1)^2 and integrating directly. Then, you can either use your initial conditions as your integration limits or plug them into find your integration constant.

 

[gonzalo12345]

I got it, I got c=1 thanks

 

[HallsofIvy]

While it is, in fact, almost trivial to separate x and y ((y-1)² and cos(\pi), in effect, are separated- they are multiplied), you don't have to find the general solution to answer (b)!

 

[kaisxuans]

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