Sr Examen
Ecuación diferencial dx*(x^3-3*x*y^2+2)-dy*(3*x^2*y-y^2)=0
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Solución
Ha introducido
[src]
3 2 d 2 2 d
2 + x + y (x)*--(y(x)) - 3*x*y (x) - 3*x *--(y(x))*y(x) = 0
dx dx
$$x^{3} - 3 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 3 x y^{2}{\left(x \right)} + y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 2 = 0$$
x^3 - 3*x^2*y*y' - 3*x*y^2 + y^2*y' + 2 = 0
Respuesta
[src]
2 / 8 \ 5 / 1408 6 \ 4 / 640 3 \
x *|3 - ---| x *|27 - ---- - --| x *|27 - ---- - --|
| 5| 3 | 10 C1| | 10 C1|
\ C1 / 2*x 40*x \ C1 / \ C1 / / 6\
y(x) = C1 + ------------ - --- - ----- + ------------------- + ------------------- + O\x /
2 2 8 4 12*C1
C1 3*C1 6*C1
$$y{\left(x \right)} = - \frac{40 x^{3}}{3 C_{1}^{8}} + \frac{x^{5} \left(27 - \frac{6}{C_{1}} - \frac{1408}{C_{1}^{10}}\right)}{6 C_{1}^{4}} - \frac{2 x}{C_{1}^{2}} + \frac{x^{4} \left(27 - \frac{3}{C_{1}} - \frac{640}{C_{1}^{10}}\right)}{12 C_{1}} + \frac{x^{2} \left(3 - \frac{8}{C_{1}^{5}}\right)}{2} + C_{1} + O\left(x^{6}\right)$$
Clasificación
factorable
1st exact
1st power series
lie group
1st exact Integral