Sr Examen
Ecuación diferencial -2*y+y'+y''=e^(2x)(2cos(x)+(-3x^2-3x-4)sin(2x))
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Solución
Ha introducido
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2
d d / / 2\ \ 2*x
-2*y(x) + --(y(x)) + ---(y(x)) = \2*cos(x) + \-4 - 3*x - 3*x /*sin(2*x)/*e
dx 2
dx
$$- 2 y{\left(x \right)} + \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = \left(\left(- 3 x^{2} - 3 x - 4\right) \sin{\left(2 x \right)} + 2 \cos{\left(x \right)}\right) e^{2 x}$$
-2*y + y' + y'' = ((-3*x^2 - 3*x - 4)*sin(2*x) + 2*cos(x))*exp(2*x)
Respuesta
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/ 2 \ 2*x
-2*x x \255*sin(2*x) + 1500*cos(x) + 1921*cos(2*x) + 2500*sin(x) - 2550*x*sin(2*x) + 510*x*cos(2*x) + 2550*x *cos(2*x)/*e
y(x) = C1*e + C2*e + ---------------------------------------------------------------------------------------------------------------------
8500
$$y{\left(x \right)} = C_{1} e^{- 2 x} + C_{2} e^{x} + \frac{\left(2550 x^{2} \cos{\left(2 x \right)} - 2550 x \sin{\left(2 x \right)} + 510 x \cos{\left(2 x \right)} + 2500 \sin{\left(x \right)} + 255 \sin{\left(2 x \right)} + 1500 \cos{\left(x \right)} + 1921 \cos{\left(2 x \right)}\right) e^{2 x}}{8500}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral