Factoring Differential

Calculus Level 2

Given $y''+y'=2y$

Where $y=e^{rx}$ . And $r$ has two distinct values (the above equation has two solutions). Find the smallest value of $r$

Clarification

-1 0 e -2

1 solution

Akhil Bansal
Dec 2, 2015

$\large \color{#3D99F6}y = e^{rx}$ $\large y' = re^{rx}= r \color{#3D99F6}y \quad , \quad y'' = r^2e^{rx} = r^2 \color{#3D99F6}y$

$\large y'' + y' = 2y$ $\large r^2 \color{#3D99F6}y + r \color{#3D99F6}y = 2 \color{#3D99F6}y$ $\large r^2 + r -2 = 0$ $\large r = 1, -2$