Question

A function $y(x)$ such that $y(0) = 1$ and $y(1) = 4e$ is a solution of the differential equation $\frac{d^2y}{dx^2} - 2\frac{dy}{dx} + y = 0$. Then, $y(2)$ is equal to _______}

• A. $-5e^2$
• B. $7e^2$
• C. $-5e$
• D. $7e$

Hint:

For repeated roots $m$, the general solution always takes the form $y(x) = (C_1 + C_2 x)e^{mx}$.
Be careful not to forget the $x$ multiplier in the second term.

Answer 1

The Correct Option is B