Sr Examen
Ecuación diferencial ydx=(ycos^2y-x)dy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d 2 d
y(x) = - x*--(y(x)) + cos (y(x))*--(y(x))*y(x)
dx dx
$$y{\left(x \right)} = - x \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} \cos^{2}{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)}$$
y = -x*y' + y*cos(y)^2*y'
Respuesta
[src]
2 2 2 2 2
sin (y(x)) cos (y(x))*y (x) sin (y(x))*y (x) cos(y(x))*sin(y(x))*y(x)
---------- + x*y(x) - ---------------- - ---------------- - ------------------------ = C1
4 4 4 2
$$x y{\left(x \right)} - \frac{y^{2}{\left(x \right)} \sin^{2}{\left(y{\left(x \right)} \right)}}{4} - \frac{y^{2}{\left(x \right)} \cos^{2}{\left(y{\left(x \right)} \right)}}{4} - \frac{y{\left(x \right)} \sin{\left(y{\left(x \right)} \right)} \cos{\left(y{\left(x \right)} \right)}}{2} + \frac{\sin^{2}{\left(y{\left(x \right)} \right)}}{4} = C_{1}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.954649230149159)
(-5.555555555555555, 1.3232818339382117)
(-3.333333333333333, 2.164208866099679)
(-1.1111111111111107, 3.5521716955316878)
(1.1111111111111107, 7.483680537255174)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 4.3149409499051355e-61)
(7.777777777777779, 8.388243571812249e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)