Sr Examen
Ecuación diferencial yx^2dy-3xy^2dx=3xdx+2ydy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 2 d d
- 3*x*y (x) + x *--(y(x))*y(x) = 3*x + 2*--(y(x))*y(x)
dx dx
$$x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 3 x y^{2}{\left(x \right)} = 3 x + 2 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
x^2*y*y' - 3*x*y^2 = 3*x + 2*y*y'
Respuesta
[src]
________________________________________
/ 6 4 2
y(x) = -\/ -1 - 8*C1 + C1*x - 6*C1*x + 12*C1*x
$$y{\left(x \right)} = - \sqrt{C_{1} x^{6} - 6 C_{1} x^{4} + 12 C_{1} x^{2} - 8 C_{1} - 1}$$
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/ 6 4 2
y(x) = \/ -1 - 8*C1 + C1*x - 6*C1*x + 12*C1*x
$$y{\left(x \right)} = \sqrt{C_{1} x^{6} - 6 C_{1} x^{4} + 12 C_{1} x^{2} - 8 C_{1} - 1}$$
Gráfico para el problema de Cauchy
Clasificación
separable
1st exact
Bernoulli
1st power series
lie group
separable Integral
1st exact Integral
Bernoulli Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -3.2210233724468313e-09)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 4.32563549789618e-37)
(7.777777777777779, 8.388243566957814e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)