Basic Differential Equation (Should be Easy)

[EstimatedEyes]

Homework Statement

Find the general solution to the differential equation.

dy/dx = 4 - y

The Attempt at a Solution

I only know how to solve them when one can multiply or divide by y. How does one take the integral of y with respect to x without the chain of y'? Thanks.

 

[lanedance]

Hi EstimatedEyes

what does y' mean? if = dy/dx, then you get 2 dy/dx = 4...?

 

[EstimatedEyes]

y' does mean dy/dx but I wrote the problem text down wrong. It should be:

dy/dx = 4 - y

 

[lanedance]

so any ideas? i think you can do this one by straight integration (with some substitution if needed...)

you need to rearrange so all the y related terms are on one side & all the x on the other side then inetgrate both sides

 

[EstimatedEyes]

Yes, I know you have to isolate the variables but don't you need dy/dx multiplied to y in order to integrate?

So you get integral(dy/dx + y) = 4x which would be easy if instead of y it was dy/dx*y but I do not know how to do it without the chain. It can't just be 1/2*y^2 can it?

The answer the book has is y = 4 + Ce^-x. How does one arrive at this?

 

[Omerta6]

Its a variable separable question.

dy/(4 - y) = dx

Integrate both sides. and solve for y

 

[EstimatedEyes]

Oh, now it's easy. Thank you Omerta6!

 

[Omerta6]

Not a problem!