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