Sr Examen
Ecuación diferencial dx*(2*x^2*y+6*y^3)=5*dy*x^4*y^2
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Solución
Ha introducido
[src]
3 2 4 2 d
6*y (x) + 2*x *y(x) = 5*x *y (x)*--(y(x))
dx
$$2 x^{2} y{\left(x \right)} + 6 y^{3}{\left(x \right)} = 5 x^{4} y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
2*x^2*y + 6*y^3 = 5*x^4*y^2*y'
Respuesta
[src]
y(x) = 0
$$y{\left(x \right)} = 0$$
______________________________________________________
/ -4
/ ----
/ / / pi*I\\ 3
____ / | 2/3 3 ____ | 4*e || 5*x
-\/ 30 * / |C1 + (-1) *\/ 10 *lowergamma|1/3, -------||*e
/ | | 3 ||
\/ \ \ 5*x //
y(x) = -----------------------------------------------------------------------
15
$$y{\left(x \right)} = - \frac{\sqrt{30} \sqrt{\left(C_{1} + \left(-1\right)^{\frac{2}{3}} \sqrt[3]{10} \gamma\left(\frac{1}{3}, \frac{4 e^{i \pi}}{5 x^{3}}\right)\right) e^{- \frac{4}{5 x^{3}}}}}{15}$$
______________________________________________________
/ -4
/ ----
/ / / pi*I\\ 3
____ / | 2/3 3 ____ | 4*e || 5*x
\/ 30 * / |C1 + (-1) *\/ 10 *lowergamma|1/3, -------||*e
/ | | 3 ||
\/ \ \ 5*x //
y(x) = ---------------------------------------------------------------------
15
$$y{\left(x \right)} = \frac{\sqrt{30} \sqrt{\left(C_{1} + \left(-1\right)^{\frac{2}{3}} \sqrt[3]{10} \gamma\left(\frac{1}{3}, \frac{4 e^{i \pi}}{5 x^{3}}\right)\right) e^{- \frac{4}{5 x^{3}}}}}{15}$$
Clasificación
factorable
Bernoulli
lie group
Bernoulli Integral