Sr Examen
Ecuación diferencial x^2*y''-2*x*y'+2*y=log(x)^2+log(x^2)
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Solución
Ha introducido
[src]
2
2 d d 2 / 2\
2*y(x) + x *---(y(x)) - 2*x*--(y(x)) = log (x) + log\x /
2 dx
dx
$$x^{2} \frac{d^{2}}{d x^{2}} y{\left(x \right)} - 2 x \frac{d}{d x} y{\left(x \right)} + 2 y{\left(x \right)} = \log{\left(x \right)}^{2} + \log{\left(x^{2} \right)}$$
x^2*y'' - 2*x*y' + 2*y = log(x)^2 + log(x^2)
Respuesta
[src]
2
13 log (x) 5*log(x) 2
y(x) = -- + ------- + -------- + C1*x + C2*x
4 2 2
$$y{\left(x \right)} = C_{1} x + C_{2} x^{2} + \frac{\log{\left(x \right)}^{2}}{2} + \frac{5 \log{\left(x \right)}}{2} + \frac{13}{4}$$
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