A student attempts to verify that is a solution to and writes the following: “Because

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A student attempts to verify that

y=x^{2}+1

is a solution to

\dfrac{dy}{dx}=2xy

and writes the following: “Because

\dfrac{dy}{dx}=2x

, we have

2x=2x(x^{2}+1)

. Cancelling

2x

from both sides gives

1=x^{2}+1

, which is true for all

x

.” Identify the specific algebraic error in the student’s argument.