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