Questions: y₁=e^(-4x), y₂=e^(4x)

y₁=e^(-4x), y₂=e^(4x)
Transcript text: $y_{1}=e^{-4 x}, y_{2}=e^{4 x}$
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Solution

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Encontrar la solución general de la ecuación diferencial lineal homogénea dada las soluciones \(y_{1}=e^{-4x}\) y \(y_{2}=e^{4x}\).

Identificación de las soluciones.

Las soluciones dadas son \(y_{1}=e^{-4x}\) y \(y_{2}=e^{4x}\).

Formación de la solución general.

La solución general se expresa como \(y = C_{1}e^{-4x} + C_{2}e^{4x}\), donde \(C_{1}\) y \(C_{2}\) son constantes arbitrarias.

\(\boxed{y = C_{1}e^{-4x} + C_{2}e^{4x}}\)

La solución general de la ecuación diferencial es \(\boxed{y = C_{1}e^{-4x} + C_{2}e^{4x}}\).

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