Sr Examen
Ecuación diferencial -tdt=(c+t/(y*2))dy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d
t*--(y(t))
d dt
-t = c*--(y(t)) + ----------
dt 2*y(t)
$$- t = c \frac{d}{d t} y{\left(t \right)} + \frac{t \frac{d}{d t} y{\left(t \right)}}{2 y{\left(t \right)}}$$
-t = c*y' + t*y'/(2*y)
Respuesta
[src]
5 / 1 \
2 4 3 t *|2 + ----|
t t t \ C1*c/ / 6\
y(t) = C1 - --- - --------- + ------- + ------------- + O\t /
2*c 2 3 2 2 3
16*C1 *c 6*C1*c 40*C1 *c
$$y{\left(t \right)} = - \frac{t^{4}}{16 C_{1}^{2} c^{3}} + \frac{t^{5} \left(2 + \frac{1}{C_{1} c}\right)}{40 C_{1}^{2} c^{3}} + \frac{t^{3}}{6 C_{1} c^{2}} - \frac{t^{2}}{2 c} + C_{1} + O\left(t^{6}\right)$$
Clasificación
factorable
1st power series
lie group