Sr Examen
Ecuación diferencial s*y'=d*(y''+a*y)-c*e^(-b*x)
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Solución
Ha introducido
[src]
/ 2 \
d | d | -b*x
s*--(y(x)) = d*|a*y(x) + ---(y(x))| - c*e
dx | 2 |
\ dx /
$$s \frac{d}{d x} y{\left(x \right)} = - c e^{- b x} + d \left(a y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)}\right)$$
s*y' = -c*exp(-b*x) + d*(a*y + y'')
Respuesta
[src]
/ _____________\ / _____________\
| / 2 2 | | / 2 2 |
x*\s - \/ s - 4*a*d / x*\s + \/ s - 4*a*d /
------------------------ ------------------------ -b*x
2*d 2*d c*e
y(x) = C1*e + C2*e + ----------------
2
a*d + b*s + d*b
$$y{\left(x \right)} = C_{1} e^{\frac{x \left(s - \sqrt{- 4 a d^{2} + s^{2}}\right)}{2 d}} + C_{2} e^{\frac{x \left(s + \sqrt{- 4 a d^{2} + s^{2}}\right)}{2 d}} + \frac{c e^{- b x}}{a d + b^{2} d + b s}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral