Sr Examen
Ecuación diferencial dx*(3*x^2*y+2*x*y+y^3)+dy*(x^2+y^2)=0
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Solución
Ha introducido
[src]
3 2 d 2 d 2
y (x) + x *--(y(x)) + y (x)*--(y(x)) + 2*x*y(x) + 3*x *y(x) = 0
dx dx
$$3 x^{2} y{\left(x \right)} + x^{2} \frac{d}{d x} y{\left(x \right)} + 2 x y{\left(x \right)} + y^{3}{\left(x \right)} + y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
3*x^2*y + x^2*y' + 2*x*y + y^3 + y^2*y' = 0
Respuesta
[src]
/ / 2 \\ / / / 2 \\ / 2 \ / 6 \\
| 2*|1 + ---|| | | 2*|1 + ---|| 4*|1 + ---| 2*|-1 + ---||
| | 2|| | | | 2|| | 2| | 2||
3 / 4 / 2 \\ 4 | 4 4 / 6 \ \ C1 /| 5 | 6 20 | 4 10 \ C1 /| \ C1 / \ C1 /|
2 / 2 \ x *|- -- - C1*|1 + ---|| x *|- -- + --- - C1*|-1 + ---| - -----------| x *|- -- + --- - C1*|1 - --- + --- + -----------| - ----------- - ------------|
x *|C1 - --| | C1 | 2|| | C1 3 | 2| C1 | | C1 3 | 4 2 2 | C1 C1 |
\ C1/ \ \ C1 // \ C1 \ C1 / / \ C1 \ C1 C1 C1 / / / 6\
y(x) = C1 + ------------ - C1*x + ------------------------ + --------------------------------------------- + ------------------------------------------------------------------------------- + O\x /
2 6 24 120
$$y{\left(x \right)} = \frac{x^{2} \left(C_{1} - \frac{2}{C_{1}}\right)}{2} + \frac{x^{3} \left(- C_{1} \left(1 + \frac{2}{C_{1}^{2}}\right) - \frac{4}{C_{1}}\right)}{6} + \frac{x^{4} \left(- C_{1} \left(-1 + \frac{6}{C_{1}^{2}}\right) - \frac{2 \left(1 + \frac{2}{C_{1}^{2}}\right)}{C_{1}} - \frac{4}{C_{1}} + \frac{4}{C_{1}^{3}}\right)}{24} + \frac{x^{5} \left(- C_{1} \left(1 + \frac{2 \left(1 + \frac{2}{C_{1}^{2}}\right)}{C_{1}^{2}} + \frac{10}{C_{1}^{2}} - \frac{4}{C_{1}^{4}}\right) - \frac{2 \left(-1 + \frac{6}{C_{1}^{2}}\right)}{C_{1}} - \frac{4 \left(1 + \frac{2}{C_{1}^{2}}\right)}{C_{1}} - \frac{6}{C_{1}} + \frac{20}{C_{1}^{3}}\right)}{120} + C_{1} - C_{1} x + O\left(x^{6}\right)$$
Clasificación
1st power series
lie group