Dar solución a las siguientes ecuaciones diferenciales de orden superior homogéneas3y´´ - 12y´ + 5y = 0?

La solucion de la ecuacion diferencial de orden superior homogeneas es : <img src="https://tex.z-dn.net/?f=y%3Dc_1e%5E%7B%5Cfrac%7B%5Cleft%286%2B%5Csqrt%7B21%7D%5Cright%29x%7D%7B3%7D%7D%2Bc_2e%5E%7B%5Cfrac%7B%5Cleft%286-%5Csqrt%7B21%7D%5Cright%29x%7D%7B3%7D%7D" />Paso a paso : Ecuacion dada : <img src="https://tex.z-dn.net/?f=3y%27%27%5C%3A-12y%27%5C%3A%2B5y%3D0" />Ecuacion lineal de segundo orden con coeficientes constantes<img src="https://tex.z-dn.net/?f=%5Cmathrm%7BUna%5C%3AEDO%5C%3Ahomogenea%2C%5C%3Alineal%5C%3Ade%5C%3Asegundo%5C%3Aorden%5C%3Atiene%5C%3Ala%5C%3Asiguiente%5C%3Aforma%5C%3A%7D%5C%3A%5C%3Aay%27%27%2Bby%27%2Bcy%3D0%5Cmathrm%7BPara%5C%3Auna%5C%3Aecuaci%C3%B3n%5C%3A%7Day%27%27%2Bby%27%2Bcy%3D0%5Cmathrm%7B%2C%5C%3Aasumir%5C%3Auna%5C%3Asoluci%C3%B3n%5C%3Acon%5C%3Ala%5C%3Aforma%5C%3A%7De%5E%7B%CE%B3x%7D" />Escribimos la ecuacion con y = e ^ {γx}<img src="https://tex.z-dn.net/?f=3%5Cleft%28%5Cleft%28e%5E%7B%CE%B3x%7D%5Cright%29%5Cright%29%27%27%5C%3A-12%5Cleft%28%5Cleft%28e%5E%7B%CE%B3x%7D%5Cright%29%5Cright%29%27%5C%3A%2B5e%5E%7B%CE%B3x%7D%3D0" /><img src="https://tex.z-dn.net/?f=%5Cmathrm%7BSimplificar%5C%3A%7D3%5Cleft%28%5Cleft%28e%5E%7B%CE%B3x%7D%5Cright%29%5Cright%29%27%27%5C%3A-12%5Cleft%28%5Cleft%28e%5E%7B%CE%B3x%7D%5Cright%29%5Cright%29%27%5C%3A%2B5e%5E%7B%CE%B3x%7D%3D0%3A%5Cquad%20e%5E%7B%CE%B3x%7D%5Cleft%283%CE%B3%5E2-12%CE%B3%2B5%5Cright%29%3D0" /><img src="https://tex.z-dn.net/?f=e%5E%7B%CE%B3x%7D%5Cleft%283%CE%B3%5E2-12%CE%B3%2B5%5Cright%29%3D0" /><img src="https://tex.z-dn.net/?f=%5Cmathrm%7BResolver%5C%3A%7D%5C%3Ae%5E%7B%CE%B3x%7D%5Cleft%283%CE%B3%5E2-12%CE%B3%2B5%5Cright%29%3D0%3A%5Cquad%20%CE%B3%3D%5Cfrac%7B6%2B%5Csqrt%7B21%7D%7D%7B3%7D%2C%5C%3A%CE%B3%3D%5Cfrac%7B6-%5Csqrt%7B21%7D%7D%7B3%7D" /><img src="https://tex.z-dn.net/?f=%CE%B3%3D%5Cfrac%7B6%2B%5Csqrt%7B21%7D%7D%7B3%7D%2C%5C%3A%CE%B3%3D%5Cfrac%7B6-%5Csqrt%7B21%7D%7D%7B3%7D" /><img src="https://tex.z-dn.net/?f=%5Cmathrm%7BPara%5C%3Ados%5C%3Araices%5C%3Areales%5C%3A%7D%CE%B3_1%5Cne%20%5C%3A%CE%B3_2%5Cmathrm%7B%2C%5C%3Ala%5C%3Asoluci%C3%B3n%5C%3Ageneral%5C%3Atoma%5C%3Ala%5C%3Aforma%3A%5Cquad%20%7Dy%3Dc_1e%5E%7B%CE%B3_1%5C%3Ax%7D%2Bc_2e%5E%7B%CE%B3_2%5C%3Ax%7Dc_1e%5E%7B%5Cfrac%7B6%2B%5Csqrt%7B21%7D%7D%7B3%7Dx%7D%2Bc_2e%5E%7B%5Cfrac%7B6-%5Csqrt%7B21%7D%7D%7B3%7Dx%7D" />Simplificando : <img src="https://tex.z-dn.net/?f=y%3Dc_1e%5E%7B%5Cfrac%7B%5Cleft%286%2B%5Csqrt%7B21%7D%5Cright%29x%7D%7B3%7D%7D%2Bc_2e%5E%7B%5Cfrac%7B%5Cleft%286-%5Csqrt%7B21%7D%5Cright%29x%7D%7B3%7D%7D" />Para mas informacion, ingresa al siguiente link : brainly.

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