e 7 : solve the following differential equation :
\[
y^{\prime \prime}-y=0
\]

Answer

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Answer

\(\boxed{y(x) = C_1 e^{-x} + C_2 e^{x}}\)

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 ：\(\boxed{y(x) = C_1 e^{-x} + C_2 e^{x}}\)