Sr Examen
Ecuación diferencial ydy=(x^2-x)(1+y^2)dx
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Solución
Ha introducido
[src]
d 2 2 2 2 --(y(x))*y(x) = x - x + x *y (x) - x*y (x) dx
$$y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = x^{2} y^{2}{\left(x \right)} + x^{2} - x y^{2}{\left(x \right)} - x$$
y*y' = x^2*y^2 + x^2 - x*y^2 - x
Respuesta
[src]
________________________
/ 2 / 2*x\
/ x *|-1 + ---|
/ \ 3 /
y(x) = -\/ -1 + C1*e
$$y{\left(x \right)} = - \sqrt{C_{1} e^{x^{2} \left(\frac{2 x}{3} - 1\right)} - 1}$$
________________________
/ 2 / 2*x\
/ x *|-1 + ---|
/ \ 3 /
y(x) = \/ -1 + C1*e
$$y{\left(x \right)} = \sqrt{C_{1} e^{x^{2} \left(\frac{2 x}{3} - 1\right)} - 1}$$
Clasificación
separable
1st exact
Bernoulli
almost linear
1st power series
lie group
separable Integral
1st exact Integral
Bernoulli Integral
almost linear Integral