Hallar la solución general de la siguiente ecuación como una serie de potencial alrededor del punto x = 0 2y'' + xy' + y = 0.
ax² + bx + c = 0
En resumen
<img src="https://tex.z-dn.net/?
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<img src="https://tex.z-dn.net/?f=%5Ctext%7Bigualando%20sub%5C%27indices%7D%5C%5C%20%5C%5C%0A4a_2%2Ba_0%2B%5Csum%5Climits_%7Bn%3D1%7D%5E%5Cinfty%202a_%7Bn%2B2%7D%28n%2B2%29%28n%2B1%29x%5E%7Bn%7D%2B%5Csum%5Climits_%7Bn%3D1%7D%5E%5Cinfty%20a_nnx%5E%7Bn%7D%2B%5Csum%5Climits_%7Bn%3D1%7D%5E%5Cinfty%20a_nx%5En%3D0%5C%5C%20%5C%5C%0A4a_2%2Ba_0%2B%5Csum%5Climits_%7Bn%3D1%7D%5E%5Cinfty%202a_%7Bn%2B2%7D%28n%2B2%29%28n%2B1%29x%5E%7Bn%7D%2B%20a_nnx%5E%7Bn%7D%2Ba_nx%5En%3D0%5C%5C%20%5C%5C%0A4a_2%2Ba_0%2B%5Csum%5Climits_%7Bn%3D1%7D%5E%5Cinfty%20%5B2a_%7Bn%2B2%7D%28n%2B2%29%2B%20a_n%5D%28n%2B1%29x%5En%3D0%5C%5C%20%5C%5C%0A" />
<img src="https://tex.z-dn.net/?f=%5Ctext%7Bcomparando%20coeficientes%3A%7D%5C%5C%20%5C%5C%0A4a_2%2Ba_0%3D0%5Cto%20a_2%3D-%5Cdfrac%7Ba_0%7D%7B4%7D%5C%5C%20%5C%5C%0A2a_%7Bn%2B2%7D%28n%2B2%29%2B%20a_n%3D0%5Cto%20a_%7Bn%2B2%7D%3D-%5Cdfrac%7Ba_n%7D%7B2%28n%2B2%29%7D%5C%3B%2C%5C%3B%20%5Cforall%20n%5Cgeq%201%5C%5C%20%5C%5C" />
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<img src="https://tex.z-dn.net/?f=a_%7B2k-1%7D%3D%5Cdfrac%7B%28-1%29%5Ek%7D%7B2%5Ek%283%5Ccdot%205%5Ccdot%207%5Ccdots%282k%2B1%29%29%7Da_1%3D%5Cdfrac%7B%28-1%29%5Ekk%21%7D%7B%282k%2B1%29%21%7Da_1%5C%5C%20%5C%5C%0Aa_%7B2k%7D%3D%5Cdfrac%7B%28-1%29%5Ek%7D%7B2%5E%7B2k-1%7Dk%21%7Da_0%5C%5C%20%5C%5C%0Ay%3D%5Csum%5Climits_%7Bn%3D0%7D%5E%5Cinfty%20a_nx%5En%5C%5C%20%5C%5C%0Ay%3D%5Csum%5Climits_%7Bn%3D0%7D%5E%5Cinfty%20a_%7B2n%7Dx%5E%7B2n%7D%2B%5Csum%5Climits_%7Bn%3D1%7D%5E%5Cinfty%20a_%7B2n-1%7Dx%5E%7B2n-1%7D%5C%5C%20%5C%5C%0A%5Cboxed%7By%3Da_0%5Csum%5Climits_%7Bn%3D0%7D%5E%5Cinfty%20%5Cdfrac%7B%28-1%29%5Ek%7D%7B2%5E%7B2k-1%7Dk%21%7Dx%5E%7B2n%7D%2Ba_1%5Csum%5Climits_%7Bn%3D1%7D%5E%5Cinfty%20%5Cdfrac%7B%28-1%29%5Ekk%21%7D%7B%282k%2B1%29%21%7Dx%5E%7B2n-1%7D%7D" />.
Se debe factorizar por diferencia de cuadrados : a ^ 2 - b ^ 2 = (a + b)(a - b) entonces : 9x ^ 2 - 16 = 0 = se escribe(3x) ^ 2 - (4) ^ 2 = 0 según esto tenemos (3x + 4)(3x - 4) = 0 las soluciones serán : (3x + 4) = 0 x…
Suerte en tu tarea : ).
Respuesta : En este caso son dos soluciones n₁ = 2 ; n₂ = - 3Explicación paso a paso : primero igualamos a ceron² + n = 6 n² + n - 6 = 0 los coeficientes son a = 1 ; b = 1 ; c = - 6 La fórmula es n₁, ₂ = - b ± √ b² - 4…
36 + x.