Sr Examen
Ecuación diferencial (ye^x+2e^x+y^2)dx+(e^x+2xy)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 x d x x d
y (x) + 2*e + --(y(x))*e + e *y(x) + 2*x*--(y(x))*y(x) = 0
dx dx
$$2 x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + y^{2}{\left(x \right)} + y{\left(x \right)} e^{x} + e^{x} \frac{d}{d x} y{\left(x \right)} + 2 e^{x} = 0$$
2*x*y*y' + y^2 + y*exp(x) + exp(x)*y' + 2*exp(x) = 0
Respuesta
[src]
______________________
/ x 2*x x
\/ C1*x - 8*x*e + e - e
y(x) = ------------------------------
2*x
$$y{\left(x \right)} = \frac{\sqrt{C_{1} x - 8 x e^{x} + e^{2 x}} - e^{x}}{2 x}$$
______________________
/ x 2*x x
- \/ C1*x - 8*x*e + e - e
y(x) = --------------------------------
2*x
$$y{\left(x \right)} = \frac{- \sqrt{C_{1} x - 8 x e^{x} + e^{2 x}} - e^{x}}{2 x}$$
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, 0.8505009488200623)
(-5.555555555555555, 1.0072589293045124)
(-3.333333333333333, 1.3125989659650732)
(-1.1111111111111107, 2.5307590495402708)
(1.1111111111111107, 7771968.834845288)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 9.144805860439919e-71)
(7.777777777777779, 8.388243567717373e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)