Question

Solve the differential equation dy/dx = (1+y)/(2+x).

Answer 1

its a separable differential equation

Answer 2

yes thats what we are studdying at the moment. but i got a mental block with this on - i dont know why>

Answer 3

We have
\[\frac{dy}{dx}= \frac{(1+y)}{(2+x)}\]
It can be rearranged as
\[\frac{dy}{1+y}=\frac{dx}{2+x}\]
Now integrate both sides
\[\int \frac{dy}{1+y}=\int \frac{dx}{2+x}\]
Can you do this?

Answer 4

yes
ln (1 + y) = ln(2 + x) + C

Answer 5

great, you are correct:)

Answer 6

i'm still confused about how you rearranged the equation initially

Answer 7

multiply by dx, then divide by 1/y+1