Question

Find y that satisfies the given condition

dy/dx=20x(5x^2-1)^3; curve passes through (1,3)

I took the antiderivative and ended up with 10x^2((5x^2-1)^4/4). I end up with a large number at the end, which I think might be wrong.

Answer 1

let
u = 5x^2-1
du = 10x dx

so, what you have is 2u^3 du
y(x) = u^4/2 = 1/2 (5x^2-1)^4 + C
y(1) = 3, so
1/2 (5-1)^4+C = 3
2C = 6-256 = -250

y(x) = 1/2 (5x^2-1)^4 - 125

Had you checked your function, you would have seen that its derivative was not the original dy/dx.