If dy/dx = (2x -1) y, y(1) = e, find y(2) A) 3 e B) 3e C) e/3 D) 3/e E) e3

Question

Please Answer ASAP!! I'm in a hurry and someone is waiting on me!

Answer 1

dy/dx = (2x-1)y

(1/y)dy = (2x-1)dx

∫(1/y)dy = ∫(2x-1)dx

lny = x²-x+C

y = e^{x^2 - x + C}

y = e^Ce^{x^2-x}

y = Ke^{x^2-x}, K = e^C

Since y = e when x = 1, e = Ke⁰. So, K = e.

y = e(e^{x^2-x})

y = e^{x^2-x+1}

So, when x = 2, y = e³.