Sr Examen
Ecuación diferencial y^2(xcosx-senx)dx-x^2(yseny+cosy)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2 2 2 d 2 d
- y (x)*sin(x) + x*y (x)*cos(x) - x *--(y(x))*cos(y(x)) - x *--(y(x))*sin(y(x))*y(x) = 0
dx dx
$$- x^{2} y{\left(x \right)} \sin{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} - x^{2} \cos{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} + x y^{2}{\left(x \right)} \cos{\left(x \right)} - y^{2}{\left(x \right)} \sin{\left(x \right)} = 0$$
-x^2*y*sin(y)*y' - x^2*cos(y)*y' + x*y^2*cos(x) - y^2*sin(x) = 0
Respuesta
[src]
-cos(y(x)) sin(x)
----------- = C1 + ------
y(x) x
$$- \frac{\cos{\left(y{\left(x \right)} \right)}}{y{\left(x \right)}} = C_{1} + \frac{\sin{\left(x \right)}}{x}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
lie group
separable Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.8408816848670386)
(-5.555555555555555, 0.7213858116789542)
(-3.333333333333333, 0.7487489645170973)
(-1.1111111111111107, 1.4086423958495364)
(1.1111111111111107, 1.4086423823253347)
(3.333333333333334, 0.7487488789347991)
(5.555555555555557, 0.7213856772595364)
(7.777777777777779, 0.8408814115652997)
(10.0, 0.7499999035774925)
(10.0, 0.7499999035774925)