Sr Examen
Ecuación diferencial dx*(-x^3+5*x*y^2)+dy*(5*x^2*y-y)=0
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Solución
Ha introducido
[src]
3 d 2 2 d
- x - --(y(x))*y(x) + 5*x*y (x) + 5*x *--(y(x))*y(x) = 0
dx dx
$$- x^{3} + 5 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 5 x y^{2}{\left(x \right)} - y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
-x^3 + 5*x^2*y*y' + 5*x*y^2 - y*y' = 0
Respuesta
[src]
___________
/ 4
___ / C1 + x
-\/ 2 * / ---------
/ 2
\/ -1 + 5*x
y(x) = -------------------------
2
$$y{\left(x \right)} = - \frac{\sqrt{2} \sqrt{\frac{C_{1} + x^{4}}{5 x^{2} - 1}}}{2}$$
___________
/ 4
___ / C1 + x
\/ 2 * / ---------
/ 2
\/ -1 + 5*x
y(x) = -----------------------
2
$$y{\left(x \right)} = \frac{\sqrt{2} \sqrt{\frac{C_{1} + x^{4}}{5 x^{2} - 1}}}{2}$$
Clasificación
1st exact
Bernoulli
1st power series
lie group
1st exact Integral
Bernoulli Integral