Sr Examen
Ecuación diferencial ((6x+1)y^2)(dy/dx)+3x^2+2y^3=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
3 2 2 d
2*y (x) + 3*x + y (x)*(1 + 6*x)*--(y(x)) = 0
dx
$$3 x^{2} + \left(6 x + 1\right) y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 2 y^{3}{\left(x \right)} = 0$$
3*x^2 + (6*x + 1)*y^2*y' + 2*y^3 = 0
Respuesta
[src]
___________
/ 3
/ C1 - 3*x
y(x) = 3 / ---------
\/ 1 + 6*x
$$y{\left(x \right)} = \sqrt[3]{\frac{C_{1} - 3 x^{3}}{6 x + 1}}$$
_________
/ 3
/ C1 - x / 3 ___ 5/6\
3 / ------- *\- \/ 3 - I*3 /
\/ 1 + 6*x
y(x) = ---------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt[3]{\frac{C_{1} - x^{3}}{6 x + 1}} \left(- \sqrt[3]{3} - 3^{\frac{5}{6}} i\right)}{2}$$
_________
/ 3
/ C1 - x / 3 ___ 5/6\
3 / ------- *\- \/ 3 + I*3 /
\/ 1 + 6*x
y(x) = ---------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt[3]{\frac{C_{1} - x^{3}}{6 x + 1}} \left(- \sqrt[3]{3} + 3^{\frac{5}{6}} i\right)}{2}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
almost linear
1st power series
lie group
1st exact Integral
almost linear Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 3.2812908145548083)
(-5.555555555555555, 4.2661475237786615)
(-3.333333333333333, 5.3526363029015585)
(-1.1111111111111107, 8.108310519670233)
(1.1111111111111107, 84908.72131719578)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 1.7373559329555976e-47)
(7.777777777777779, 8.388243567720347e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)