Sr Examen
Ecuación diferencial (e^y)*(1+x^2)dy-2x*(1+e^y)dx=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d y(x) y(x) 2 d y(x)
-2*x + --(y(x))*e - 2*x*e + x *--(y(x))*e = 0
dx dx
$$x^{2} e^{y{\left(x \right)}} \frac{d}{d x} y{\left(x \right)} - 2 x e^{y{\left(x \right)}} - 2 x + e^{y{\left(x \right)}} \frac{d}{d x} y{\left(x \right)} = 0$$
x^2*exp(y)*y' - 2*x*exp(y) - 2*x + exp(y)*y' = 0
Respuesta
[src]
/ 2\ y(x) = log\-1 + C1 + C1*x /
$$y{\left(x \right)} = \log{\left(C_{1} x^{2} + C_{1} - 1 \right)}$$
Gráfico para el problema de Cauchy
Clasificación
separable
1st exact
almost linear
1st power series
lie group
separable Integral
1st exact Integral
almost linear Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -0.10782511605369069)
(-5.555555555555555, -35.027276439671795)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 6.971028255580836e+173)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 6.29567287026948e-66)
(7.777777777777779, 8.388243567354547e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)