Sr Examen
Ecuación diferencial 6*dx*x-6*dy*y=-3*dx*x*y^2+2*dy*x^2*y
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Solución
Ha introducido
[src]
d 2 2 d
6*x - 6*--(y(x))*y(x) = - 3*x*y (x) + 2*x *--(y(x))*y(x)
dx dx
$$6 x - 6 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 2 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 3 x y^{2}{\left(x \right)}$$
6*x - 6*y*y' = 2*x^2*y*y' - 3*x*y^2
Respuesta
[src]
_________________________________________________
/ ________ ________
/ / 2 2*C1 2 / 2 2*C1
y(x) = -\/ -2 + 3*\/ 3 + x *e + x *\/ 3 + x *e
$$y{\left(x \right)} = - \sqrt{x^{2} \sqrt{x^{2} + 3} e^{2 C_{1}} + 3 \sqrt{x^{2} + 3} e^{2 C_{1}} - 2}$$
_________________________________________________
/ ________ ________
/ / 2 2*C1 2 / 2 2*C1
y(x) = \/ -2 + 3*\/ 3 + x *e + x *\/ 3 + x *e
$$y{\left(x \right)} = \sqrt{x^{2} \sqrt{x^{2} + 3} e^{2 C_{1}} + 3 \sqrt{x^{2} + 3} e^{2 C_{1}} - 2}$$
Clasificación
factorable
separable
1st exact
Bernoulli
1st power series
lie group
separable Integral
1st exact Integral
Bernoulli Integral