Sr Examen
Ecuaciones diferenciales/
dx*(9*x^2*y^4-2*x*y^3+y^6+2*y-23)+dy*(12*x^3*y^3-3*x^2*y^2+6*x*y^5+2*x+47)=0
Ecuación diferencial dx*(9*x^2*y^4-2*x*y^3+y^6+2*y-23)+dy*(12*x^3*y^3-3*x^2*y^2+6*x*y^5+2*x+47)=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
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6 d 3 d 2 4 2 2 d 5 d 3 3 d
-23 + y (x) + 2*y(x) + 47*--(y(x)) - 2*x*y (x) + 2*x*--(y(x)) + 9*x *y (x) - 3*x *y (x)*--(y(x)) + 6*x*y (x)*--(y(x)) + 12*x *y (x)*--(y(x)) = 0
dx dx dx dx dx
$$12 x^{3} y^{3}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 9 x^{2} y^{4}{\left(x \right)} - 3 x^{2} y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 6 x y^{5}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 2 x y^{3}{\left(x \right)} + 2 x \frac{d}{d x} y{\left(x \right)} + y^{6}{\left(x \right)} + 2 y{\left(x \right)} + 47 \frac{d}{d x} y{\left(x \right)} - 23 = 0$$
12*x^3*y^3*y' + 9*x^2*y^4 - 3*x^2*y^2*y' + 6*x*y^5*y' - 2*x*y^3 + 2*x*y' + y^6 + 2*y + 47*y' - 23 = 0
Respuesta
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/ 6 \ 2 3 3 4 47*y(x) + x*\-23 + y (x) + 2*y(x)/ - x *y (x) + 3*x *y (x) = C1
$$3 x^{3} y^{4}{\left(x \right)} - x^{2} y^{3}{\left(x \right)} + x \left(y^{6}{\left(x \right)} + 2 y{\left(x \right)} - 23\right) + 47 y{\left(x \right)} = C_{1}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
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(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.8942614531773079)
(-5.555555555555555, 1.1352470034856244)
(-3.333333333333333, 1.625606752106251)
(-1.1111111111111107, 2.8503726838958805)
(1.1111111111111107, 2272.135492202349)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 6.446773053330691e-67)
(7.777777777777779, 8.388243571809644e+296)
(10.0, 9.036991477623112e-277)
(10.0, 9.036991477623112e-277)