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?

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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?

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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?
No, because you have to put the +C on after you integrate, but before you do any algebra.
You can put it on either side, but you can't wait until after you rearrange things.

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ok cool. thanks

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