Sr Examen
Ecuación diferencial y'''+2y''-5y'-6y=3x^2+e^(2x)
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Solución
Ha introducido
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2 3
d d d 2 2*x
-6*y(x) - 5*--(y(x)) + 2*---(y(x)) + ---(y(x)) = 3*x + e
dx 2 3
dx dx
$$- 6 y{\left(x \right)} - 5 \frac{d}{d x} y{\left(x \right)} + 2 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 3 x^{2} + e^{2 x}$$
-6*y - 5*y' + 2*y'' + y''' = 3*x^2 + exp(2*x)
Respuesta
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2
37 x 5*x -3*x -x / x \ 2*x
y(x) = - -- - -- + --- + C2*e + C3*e + |C1 + --|*e
36 2 6 \ 15/
$$y{\left(x \right)} = C_{2} e^{- 3 x} + C_{3} e^{- x} - \frac{x^{2}}{2} + \frac{5 x}{6} + \left(C_{1} + \frac{x}{15}\right) e^{2 x} - \frac{37}{36}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral