Sr Examen
Ecuación diferencial dx*(2*x*y^2-3)+dy*(2*x^2*y+4)=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d 2 2 d
-3 + 4*--(y(x)) + 2*x*y (x) + 2*x *--(y(x))*y(x) = 0
dx dx
$$2 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 2 x y^{2}{\left(x \right)} + 4 \frac{d}{d x} y{\left(x \right)} - 3 = 0$$
2*x^2*y*y' + 2*x*y^2 + 4*y' - 3 = 0
Respuesta
[src]
__________________
/ 3 2
-2 + \/ 4 + 3*x + C1*x
y(x) = --------------------------
2
x
$$y{\left(x \right)} = \frac{\sqrt{C_{1} x^{2} + 3 x^{3} + 4} - 2}{x^{2}}$$
__________________
/ 3 2
-2 - \/ 4 + 3*x + C1*x
y(x) = --------------------------
2
x
$$y{\left(x \right)} = \frac{- \sqrt{C_{1} x^{2} + 3 x^{3} + 4} - 2}{x^{2}}$$
Clasificación
1st exact
1st power series
lie group
1st exact Integral