Question

Solve the differential equation

xy+y'=100x

Answer 1

\[y'+xy=100x \\ \text{ integrating factor is } e^{\int_0^x\limits t dt}\]
some times people like to call it \[e^{\int\limits x dx}\]
but we don't need the constant of integration
that is take the constant of integration to be 0

Answer 2

\[v y'+v xy =v 100 x \\ \text{ where we will pretend } v \text{ is what you got for the integrating factor } \\ (vy)'=v100x\]
find v
replace v
then integrate both sides of that equation

Answer 3

Or \[\frac{y'}{100-y}=x.\]Pick your posion

Answer 4

oh clever
didn't even try to see if seperable

Answer 5

I was wondering if it was also a separable equation as well

Answer 6

I'm mainly doing the problem through the separable method.

Answer 7

seem like it is

xy+y'=100x
y'=100x-xy
y'=x(100-y)
y'/ (100-y) = x
and then integrate both sides
dy/(100-y) = x dx

Answer 8

it's always the rhs side of the equation to be the easiest part

Answer 9

When I integrate dy/100-y shouldn't I just get ln(100-y)?

Answer 10

let's see.. we can use u sub and the log antiderivative