Sr Examen
Ecuación diferencial (x^2)y''+2xy'-12y=(x^3)ln(x)
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Solución
Ha introducido
[src]
2
2 d d 3
-12*y(x) + x *---(y(x)) + 2*x*--(y(x)) = x *log(x)
2 dx
dx
$$x^{2} \frac{d^{2}}{d x^{2}} y{\left(x \right)} + 2 x \frac{d}{d x} y{\left(x \right)} - 12 y{\left(x \right)} = x^{3} \log{\left(x \right)}$$
x^2*y'' + 2*x*y' - 12*y = x^3*log(x)
Respuesta
[src]
7 / 2 \
x *\C2 - 2*log(x) + 7*log (x)/
C1 + ------------------------------
98
y(x) = -----------------------------------
4
x
$$y{\left(x \right)} = \frac{C_{1} + \frac{x^{7} \left(C_{2} + 7 \log{\left(x \right)}^{2} - 2 \log{\left(x \right)}\right)}{98}}{x^{4}}$$
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