Sr Examen
Ecuación diferencial y''-(5cosx)y'-5y=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2
d d
-5*y(x) - 5*--(y(x))*cos(x) + ---(y(x)) = 0
dx 2
dx
$$- 5 y{\left(x \right)} - 5 \cos{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = 0$$
-5*y - 5*cos(x)*y' + y'' = 0
Respuesta
[src]
/ 2 4 3 4 2 \ / 2 2 2 3 3 3 \
| 5*x 25*x 25*x *cos(x) 125*x *cos (x)| | 5*x 5*x*cos(x) 25*x *cos (x) 25*x *cos(x) 125*x *cos (x)| / 6\
y(x) = C2*|1 + ---- + ----- + ------------ + --------------| + C1*x*|1 + ---- + ---------- + ------------- + ------------ + --------------| + O\x /
\ 2 24 6 24 / \ 6 2 6 12 24 /
$$y{\left(x \right)} = C_{2} \left(\frac{125 x^{4} \cos^{2}{\left(x \right)}}{24} + \frac{25 x^{4}}{24} + \frac{25 x^{3} \cos{\left(x \right)}}{6} + \frac{5 x^{2}}{2} + 1\right) + C_{1} x \left(\frac{125 x^{3} \cos^{3}{\left(x \right)}}{24} + \frac{25 x^{3} \cos{\left(x \right)}}{12} + \frac{25 x^{2} \cos^{2}{\left(x \right)}}{6} + \frac{5 x^{2}}{6} + \frac{5 x \cos{\left(x \right)}}{2} + 1\right) + O\left(x^{6}\right)$$
Clasificación
2nd power series ordinary