Sr Examen
Ecuación diferencial (x*sin(x)+cos(x))*y''-x*cos(x)*y'+y*cos(x)=0
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Solución
Ha introducido
[src]
2
d d
(x*sin(x) + cos(x))*---(y(x)) + cos(x)*y(x) - x*--(y(x))*cos(x) = 0
2 dx
dx
$$- x \cos{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \left(x \sin{\left(x \right)} + \cos{\left(x \right)}\right) \frac{d^{2}}{d x^{2}} y{\left(x \right)} + y{\left(x \right)} \cos{\left(x \right)} = 0$$
-x*cos(x)*y' + (x*sin(x) + cos(x))*y'' + y*cos(x) = 0
Respuesta
[src]
/ 2 4 4 2 3 \
| x x x *tan (x) x *tan(x)| / 6\
y(x) = C1*x + C2*|1 - -- - -- - ---------- + ---------| + O\x /
\ 2 24 12 6 /
$$y{\left(x \right)} = C_{2} \left(- \frac{x^{4} \tan^{2}{\left(x \right)}}{12} - \frac{x^{4}}{24} + \frac{x^{3} \tan{\left(x \right)}}{6} - \frac{x^{2}}{2} + 1\right) + C_{1} x + O\left(x^{6}\right)$$
Clasificación
2nd power series ordinary