- #1

gingermom

Gold Member

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## Homework Statement

dy/dx = (1+x)/xy solve y(1) = -4

## Homework Equations

## The Attempt at a Solution

What threw me was the solve for if y(1) = -4I grouped variables and then integrated both sides and solved for y.

(1/2)y^2 = ln|x|+x+c

y=+- √2ln|x|+x+c

I then switched the x and y to get the inverse of the equation and set that equal to -4

-4=-+ √2ln1+1+c

16= 2*(1+c)

8-1=c

7=c

However, I am not sure this was the correct approach. I could not figure out how to isolate x in the beginning, but I am not 100 percent sure of my logic of using the inverse, and whether I applied it appropriately. If this is way off base, can you point me in the correct direction? We have not had any problems quite like this and I am not sure I am making the correct leap in combining concepts.

Thanks.