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