Sr Examen
Ecuación diferencial cosxdx-cosydy=xcosxdx+ydy
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d d - --(y(x))*cos(y(x)) + cos(x) = x*cos(x) + --(y(x))*y(x) dx dx
$$\cos{\left(x \right)} - \cos{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} = x \cos{\left(x \right)} + y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
cos(x) - cos(y)*y' = x*cos(x) + y*y'
Respuesta
[src]
2 y (x) ----- - sin(x) + x*sin(x) + cos(x) + sin(y(x)) = C1 2
$$x \sin{\left(x \right)} + \frac{y^{2}{\left(x \right)}}{2} - \sin{\left(x \right)} + \sin{\left(y{\left(x \right)} \right)} + \cos{\left(x \right)} = C_{1}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st exact
1st power series
lie group
separable Integral
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -0.7390851125205026)
(-5.555555555555555, 6.91571558639996e-310)
(-3.333333333333333, 6.9157155876545e-310)
(-1.1111111111111107, 6.9157155864031e-310)
(1.1111111111111107, 6.9157155871019e-310)
(3.333333333333334, 6.9157155864063e-310)
(5.555555555555557, 6.91571558765844e-310)
(7.777777777777779, 6.91571558640944e-310)
(10.0, 6.9157155859225e-310)
(10.0, 6.9157155859225e-310)