e 7 : solve the following differential equation :
$y^{''} - y = 0$

Answer

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Answer

$y (x) = C_{1} e^{- x} + C_{2} e^{x}$

Steps

Step 1 ：Find the characteristic equation: $r^{2} - 1 = 0$

Step 2 ：Find the roots: $r_{1} = - 1$ and $r_{2} = 1$

Step 3 ：Write the general solution: $y (x) = C_{1} e^{- x} + C_{2} e^{x}$

Step 4 ： $y (x) = C_{1} e^{- x} + C_{2} e^{x}$