Sr Examen
Ecuación diferencial (e^(xy)*y+1/ycosx/y)dx+(e^(xy)*x-x/y^2cosx/y+y)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d
x*--(y(x))*cos(x)
cos(x) d x*y(x) d x*y(x) dx
------ + --(y(x))*y(x) + e *y(x) + x*--(y(x))*e - ----------------- = 0
2 dx dx 3
y (x) y (x)
$$x e^{x y{\left(x \right)}} \frac{d}{d x} y{\left(x \right)} - \frac{x \cos{\left(x \right)} \frac{d}{d x} y{\left(x \right)}}{y^{3}{\left(x \right)}} + y{\left(x \right)} e^{x y{\left(x \right)}} + y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \frac{\cos{\left(x \right)}}{y^{2}{\left(x \right)}} = 0$$
x*exp(x*y)*y' - x*cos(x)*y'/y^3 + y*exp(x*y) + y*y' + cos(x)/y^2 = 0
Gráfico para el problema de Cauchy
Clasificación
factorable
1st power series
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.43802349097166055)
(-5.555555555555555, 0.3121046272039505)
(-3.333333333333333, 0.015981017689509384)
(-1.1111111111111107, 0.005327028330274477)
(1.1111111111111107, -0.005327032052955162)
(3.333333333333334, -0.015981117093071207)
(5.555555555555557, -0.022595191691839496)
(7.777777777777779, 8.388243571828606e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)