Show that the given function is a solution of the differential equation. dy dx + 8y = 6e-5x, y = = 3e II -6x Substituting and y into the original equation gives + 8(3e-6x) = 6e-6x. The solution checks.

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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Show that the given function is a solution of the differential equation.

**Please refer to attachment

Show that the given function is a solution of the differential equation.

\[
\frac{dy}{dx} + 8y = 6e^{-6x}, \quad y = 3e^{-6x}
\]

\[
\frac{dy}{dx} = \text{\_\_\_\_\_\_\_\_\_} \, (\text{red cross})
\]

Substituting \(\frac{dy}{dx}\) and \(y\) into the original equation gives

\[
\text{\_\_\_\_\_\_\_\_\_} + 8(3e^{-6x}) = 6e^{-6x}
\]

The solution checks.
Transcribed Image Text:Show that the given function is a solution of the differential equation. \[ \frac{dy}{dx} + 8y = 6e^{-6x}, \quad y = 3e^{-6x} \] \[ \frac{dy}{dx} = \text{\_\_\_\_\_\_\_\_\_} \, (\text{red cross}) \] Substituting \(\frac{dy}{dx}\) and \(y\) into the original equation gives \[ \text{\_\_\_\_\_\_\_\_\_} + 8(3e^{-6x}) = 6e^{-6x} \] The solution checks.
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