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