Sr Examen
Ecuación diferencial dx*(3*x^2+6*x*y^2)+dy*(6*x^2*y+4*y^3)=0
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Solución
Ha introducido
[src]
2 3 d 2 2 d
3*x + 4*y (x)*--(y(x)) + 6*x*y (x) + 6*x *--(y(x))*y(x) = 0
dx dx
$$6 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 3 x^{2} + 6 x y^{2}{\left(x \right)} + 4 y^{3}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
6*x^2*y*y' + 3*x^2 + 6*x*y^2 + 4*y^3*y' = 0
Respuesta
[src]
________________________________
/ __________________
___ / / 3 4 2
-\/ 2 *\/ - \/ C1 - 4*x + 9*x - 3*x
y(x) = --------------------------------------------
2
$$y{\left(x \right)} = - \frac{\sqrt{2} \sqrt{- 3 x^{2} - \sqrt{C_{1} + 9 x^{4} - 4 x^{3}}}}{2}$$
________________________________
/ __________________
___ / / 3 4 2
\/ 2 *\/ - \/ C1 - 4*x + 9*x - 3*x
y(x) = ------------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt{2} \sqrt{- 3 x^{2} - \sqrt{C_{1} + 9 x^{4} - 4 x^{3}}}}{2}$$
______________________________
/ __________________
___ / / 3 4 2
-\/ 2 *\/ \/ C1 - 4*x + 9*x - 3*x
y(x) = ------------------------------------------
2
$$y{\left(x \right)} = - \frac{\sqrt{2} \sqrt{- 3 x^{2} + \sqrt{C_{1} + 9 x^{4} - 4 x^{3}}}}{2}$$
______________________________
/ __________________
___ / / 3 4 2
\/ 2 *\/ \/ C1 - 4*x + 9*x - 3*x
y(x) = ----------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt{2} \sqrt{- 3 x^{2} + \sqrt{C_{1} + 9 x^{4} - 4 x^{3}}}}{2}$$
Clasificación
1st exact
1st power series
lie group
1st exact Integral