Sr Examen
Ecuación diferencial yy'=1-2x/y
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d 2*x --(y(x))*y(x) = 1 - ---- dx y(x)
$$y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = - \frac{2 x}{y{\left(x \right)}} + 1$$
y*y' = -2*x/y + 1
Respuesta
[src]
/ / 3 \\ / / 3 \ / 9 \\
| 5*|-8 - --|| | 5*|-8 - --| 10*|20 + --||
2 / 1 \ 3 / 3 \ 4 | 30 \ C1/| 5 | 390 \ C1/ \ C1/|
x *|-2 - --| x *|10 + --| x *|-24 - -- + -----------| x *|496 + --- - ----------- + ------------|
x \ C1/ \ C1/ \ C1 C1 / \ C1 C1 C1 / / 6\
y(x) = C1 + -- + ------------ + ------------ + --------------------------- + ------------------------------------------- + O\x /
C1 2 4 5 7
2*C1 6*C1 24*C1 120*C1
$$y{\left(x \right)} = \frac{x^{5} \left(496 - \frac{5 \left(-8 - \frac{3}{C_{1}}\right)}{C_{1}} + \frac{10 \left(20 + \frac{9}{C_{1}}\right)}{C_{1}} + \frac{390}{C_{1}}\right)}{120 C_{1}^{7}} + \frac{x^{4} \left(-24 + \frac{5 \left(-8 - \frac{3}{C_{1}}\right)}{C_{1}} - \frac{30}{C_{1}}\right)}{24 C_{1}^{5}} + \frac{x^{3} \left(10 + \frac{3}{C_{1}}\right)}{6 C_{1}^{4}} + \frac{x^{2} \left(-2 - \frac{1}{C_{1}}\right)}{2 C_{1}^{2}} + \frac{x}{C_{1}} + C_{1} + O\left(x^{6}\right)$$
Clasificación
1st power series
lie group