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!! In a math battle and I haven’t learned this yet!!

Answer 1

This differential equation can be solved by separating variables.

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

Integrate both sides

ln y = x² - x + C

y=Aexp(x² - x) where C = lnA

SInce y(1) = e, A = e

and y(x) =exp(x² - x +1 and y(2) = e³