Always Excited to Solve Differential Equations

Calculus Level 4

$\large \dfrac{d^2y}{dx^2} = y$

A function $y = f(x)$ satisfies the above differential equation with $y(0) = 1$ and $y(2) = 5$ .

What is $\left \lfloor y(3) \right\rfloor$ ?

13 7 9 11

1 solution

Steven Chase
May 25, 2018

By inspection, the general solution should be:

$y = A e^x + B e^{-x}$

Initial conditions yield the following equations:

$1 = A + B \\ 5 = A e^2 + B e^{-2}$

Solve the linear system for $A$ and $B$ , and then evaluate $y(3)$ . This comes out to $\approx 13.487$