Differential equations question:
solve:
dy/dx = 4x^3y^2, y(1)=-.5

I got -x^(-4) + 1/2 = y
Wolfram and book got -(x^4+1)^(-1) = y

Am I right?

Question

Differential equations question:
solve:
dy/dx = 4x^3y^2, y(1)=-.5

I got -x^(-4) + 1/2 = y
Wolfram and book got -(x^4+1)^(-1) = y

Am I right?

anonymous · Answer

after I integrate both sides, I get 
-1/y = x^4
The book put a +C on the x^4, and used that to solve that. Their C was 1
I rearranged the equation to y= -1/x^4, and then added the C. My C was 1/2

Is that legal?

anonymous · Answer

No, because you have to put the +C on after you integrate, but before you do any algebra.

anonymous · Answer

You can put it on either side, but you can't wait until after you rearrange things.

anonymous · Answer

ok cool. thanks