Sr Examen
Ecuación diferencial ay’’’’+by’’’+cy’’+dy’+f=0
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Solución
Ha introducido
[src]
4 3 2
d d d
f + a*---(y(x)) + b*---(y(x)) + c*---(y(x)) = 0
4 3 2
dx dx dx
$$a \frac{d^{4}}{d x^{4}} y{\left(x \right)} + b \frac{d^{3}}{d x^{3}} y{\left(x \right)} + c \frac{d^{2}}{d x^{2}} y{\left(x \right)} + f = 0$$
a*y'''' + b*y''' + c*y'' + f = 0
Respuesta
[src]
/ ____________\ / ____________ \
| / 2 | | / 2 |
x*\-b - \/ b - 4*a*c / x*\\/ b - 4*a*c - b/
------------------------ ----------------------- 2
2*a 2*a f*x
y(x) = C1 + C2*x + C3*e + C4*e - ----
2*c
$$y{\left(x \right)} = C_{1} + C_{2} x + C_{3} e^{\frac{x \left(- b - \sqrt{- 4 a c + b^{2}}\right)}{2 a}} + C_{4} e^{\frac{x \left(- b + \sqrt{- 4 a c + b^{2}}\right)}{2 a}} - \frac{f x^{2}}{2 c}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth order reducible
nth linear constant coeff variation of parameters Integral