Sr Examen
Ecuación diferencial -4*y+3*y'+y''=e^(4*x)*((3*x^2-5*x-3)*sin(2*x)+3*cos(5*x))
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Solución
Ha introducido
[src]
2
d d / / 2\ \ 4*x
-4*y(x) + 3*--(y(x)) + ---(y(x)) = \3*cos(5*x) + \-3 - 5*x + 3*x /*sin(2*x)/*e
dx 2
dx
$$- 4 y{\left(x \right)} + 3 \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = \left(\left(3 x^{2} - 5 x - 3\right) \sin{\left(2 x \right)} + 3 \cos{\left(5 x \right)}\right) e^{4 x}$$
-4*y + 3*y' + y'' = ((3*x^2 - 5*x - 3)*sin(2*x) + 3*cos(5*x))*exp(4*x)
Respuesta
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/ 2 2 \ 4*x
-4*x x \-221975167*sin(2*x) - 50396161*cos(2*x) - 3809598*cos(5*x) + 209527890*sin(5*x) - 511275986*x*sin(2*x) - 286892034*x *cos(2*x) + 260810940*x *sin(2*x) + 773660446*x*cos(2*x)/*e
y(x) = C1*e + C2*e + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3842614516
$$y{\left(x \right)} = C_{1} e^{- 4 x} + C_{2} e^{x} + \frac{\left(260810940 x^{2} \sin{\left(2 x \right)} - 286892034 x^{2} \cos{\left(2 x \right)} - 511275986 x \sin{\left(2 x \right)} + 773660446 x \cos{\left(2 x \right)} - 221975167 \sin{\left(2 x \right)} + 209527890 \sin{\left(5 x \right)} - 50396161 \cos{\left(2 x \right)} - 3809598 \cos{\left(5 x \right)}\right) e^{4 x}}{3842614516}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral