Sr Examen
Ecuación diferencial y"-tg(x)y'+5y=0
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Solución
Ha introducido
[src]
2
d d
5*y(x) - --(y(x))*tan(x) + ---(y(x)) = 0
dx 2
dx
$$5 y{\left(x \right)} - \tan{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = 0$$
5*y - tan(x)*y' + y'' = 0
Respuesta
[src]
/ 2 4 3 4 2 \ / 2 3 2 2 3 3 \
| 5*x 25*x 5*x *tan(x) 5*x *tan (x)| | 5*x x*tan(x) 5*x *tan(x) x *tan (x) x *tan (x)| / 6\
y(x) = C2*|1 - ---- + ----- - ----------- - ------------| + C1*x*|1 - ---- + -------- - ----------- + ---------- + ----------| + O\x /
\ 2 24 6 24 / \ 6 2 12 6 24 /
$$y{\left(x \right)} = C_{2} \left(- \frac{5 x^{4} \tan^{2}{\left(x \right)}}{24} + \frac{25 x^{4}}{24} - \frac{5 x^{3} \tan{\left(x \right)}}{6} - \frac{5 x^{2}}{2} + 1\right) + C_{1} x \left(\frac{x^{3} \tan^{3}{\left(x \right)}}{24} - \frac{5 x^{3} \tan{\left(x \right)}}{12} + \frac{x^{2} \tan^{2}{\left(x \right)}}{6} - \frac{5 x^{2}}{6} + \frac{x \tan{\left(x \right)}}{2} + 1\right) + O\left(x^{6}\right)$$
Clasificación
2nd power series ordinary