Sr Examen
Ecuación diferencial xy''+x(y')2=y'
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Solución
Ha introducido
[src]
2
d d d
x*---(y(x)) + 2*x*--(y(x)) = --(y(x))
2 dx dx
dx
$$2 x \frac{d}{d x} y{\left(x \right)} + x \frac{d^{2}}{d x^{2}} y{\left(x \right)} = \frac{d}{d x} y{\left(x \right)}$$
2*x*y' + x*y'' = y'
Respuesta
[src]
2 - 2*re(x) y(x) = C1 + x *(C2*sin(2*|im(x)|*log(x)) + C3*cos(2*im(x)*log(x)))
$$y{\left(x \right)} = C_{1} + x^{2 - 2 \operatorname{re}{\left(x\right)}} \left(C_{2} \sin{\left(2 \log{\left(x \right)} \left|{\operatorname{im}{\left(x\right)}}\right| \right)} + C_{3} \cos{\left(2 \log{\left(x \right)} \operatorname{im}{\left(x\right)} \right)}\right)$$
Clasificación
nth linear euler eq homogeneous
nth order reducible
2nd power series regular