Sr Examen
Ecuación diferencial (3*x^2*y*e^y+2*cosy)dx+(x^3*e^y*y+x^3*e^y-2*x*seny)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
3 d y(x) d 2 y(x) 3 d y(x)
2*cos(y(x)) + x *--(y(x))*e - 2*x*--(y(x))*sin(y(x)) + 3*x *e *y(x) + x *--(y(x))*e *y(x) = 0
dx dx dx
$$x^{3} y{\left(x \right)} e^{y{\left(x \right)}} \frac{d}{d x} y{\left(x \right)} + x^{3} e^{y{\left(x \right)}} \frac{d}{d x} y{\left(x \right)} + 3 x^{2} y{\left(x \right)} e^{y{\left(x \right)}} - 2 x \sin{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} + 2 \cos{\left(y{\left(x \right)} \right)} = 0$$
x^3*y*exp(y)*y' + x^3*exp(y)*y' + 3*x^2*y*exp(y) - 2*x*sin(y)*y' + 2*cos(y) = 0
Respuesta
[src]
/ 2 y(x) \ x*\2*cos(y(x)) + x *e *y(x)/ = C1
$$x \left(x^{2} y{\left(x \right)} e^{y{\left(x \right)}} + 2 \cos{\left(y{\left(x \right)} \right)}\right) = C_{1}$$
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, 1.1135699435851651)
(-5.555555555555555, 1.7032371846738878)
(-3.333333333333333, 2.757026348714806)
(-1.1111111111111107, 5.379680384655105)
(1.1111111111111107, 136.94722148642634)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 3.4667248631491264e+179)
(7.777777777777779, 8.388243567356334e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)