Sr Examen
Ecuación diferencial x^3y'''-3x^2y''+6xy'-6y=3+ln(x^3)
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Solución
Ha introducido
[src]
3 2
3 d 2 d d / 3\
-6*y(x) + x *---(y(x)) - 3*x *---(y(x)) + 6*x*--(y(x)) = 3 + log\x /
3 2 dx
dx dx
$$x^{3} \frac{d^{3}}{d x^{3}} y{\left(x \right)} - 3 x^{2} \frac{d^{2}}{d x^{2}} y{\left(x \right)} + 6 x \frac{d}{d x} y{\left(x \right)} - 6 y{\left(x \right)} = \log{\left(x^{3} \right)} + 3$$
x^3*y''' - 3*x^2*y'' + 6*x*y' - 6*y = log(x^3) + 3
Respuesta
[src]
17 log(x) 2 3
y(x) = - -- - ------ + C1*x + C2*x + C3*x
12 2
$$y{\left(x \right)} = C_{1} x + C_{2} x^{2} + C_{3} x^{3} - \frac{\log{\left(x \right)}}{2} - \frac{17}{12}$$
Clasificación
nth linear euler eq nonhomogeneous undetermined coefficients
nth linear euler eq nonhomogeneous variation of parameters
nth linear euler eq nonhomogeneous variation of parameters Integral