Sr Examen
Ecuación diferencial dx*(-x^2*y^7*sin(2*x)-3)/(3*x^2*y^4)+dy*(x*y^7*cos(x)^2-4)/(x*y^5)=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d
3 4*--(y(x))
1 y (x)*sin(2*x) 2 2 d dx
- -------- - -------------- + cos (x)*y (x)*--(y(x)) - ---------- = 0
2 4 3 dx 5
x *y (x) x*y (x)
$$- \frac{y^{3}{\left(x \right)} \sin{\left(2 x \right)}}{3} + y^{2}{\left(x \right)} \cos^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - \frac{4 \frac{d}{d x} y{\left(x \right)}}{x y^{5}{\left(x \right)}} - \frac{1}{x^{2} y^{4}{\left(x \right)}} = 0$$
-y^3*sin(2*x)/3 + y^2*cos(x)^2*y' - 4*y'/(x*y^5) - 1/(x^2*y^4) = 0
Respuesta
[src]
3 / 2 \ 3 1 y (x)*\-cos(2*x) + 2*cos (x)/ y (x)*cos(2*x) ------- + ----------------------------- + -------------- = C1 4 6 6 x*y (x)
$$\frac{\left(2 \cos^{2}{\left(x \right)} - \cos{\left(2 x \right)}\right) y^{3}{\left(x \right)}}{6} + \frac{y^{3}{\left(x \right)} \cos{\left(2 x \right)}}{6} + \frac{1}{x y^{4}{\left(x \right)}} = C_{1}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.8759949920414851)
(-5.555555555555555, 0.8568240263981126)
(-3.333333333333333, 0.902150998296717)
(-1.1111111111111107, 1.266123256580684)
(1.1111111111111107, 534.653803078769)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 7.566503212566957e-67)
(7.777777777777779, 8.388243571812622e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)