Sr Examen
Ecuación diferencial (1-2x^2-2y)y'=4x^3+4xy
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Solución
Ha introducido
[src]
/ 2 \ d 3
\1 - 2*x - 2*y(x)/*--(y(x)) = 4*x + 4*x*y(x)
dx
$$\left(- 2 x^{2} - 2 y{\left(x \right)} + 1\right) \frac{d}{d x} y{\left(x \right)} = 4 x^{3} + 4 x y{\left(x \right)}$$
(-2*x^2 - 2*y + 1)*y' = 4*x^3 + 4*x*y
Respuesta
[src]
/ / 2*C1 \\
| 2*C1*|-1 + ---------||
4 | 2*C1 \ -1 + 2*C1/|
x *|-1 + --------- - ---------------------| 2
\ -1 + 2*C1 -1 + 2*C1 / 2*C1*x / 6\
y(x) = C1 + ------------------------------------------- - --------- + O\x /
-1 + 2*C1 -1 + 2*C1
$$y{\left(x \right)} = \frac{x^{4} \left(- \frac{2 C_{1} \left(\frac{2 C_{1}}{2 C_{1} - 1} - 1\right)}{2 C_{1} - 1} + \frac{2 C_{1}}{2 C_{1} - 1} - 1\right)}{2 C_{1} - 1} + C_{1} - \frac{2 C_{1} x^{2}}{2 C_{1} - 1} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 40.45301774137763)
(-5.555555555555555, 70.23002807708625)
(-3.333333333333333, 90.08124882544442)
(-1.1111111111111107, 100.0068236991287)
(1.1111111111111107, 100.00682372921119)
(3.333333333333334, 90.0812492969643)
(5.555555555555557, 70.23002870354888)
(7.777777777777779, 40.45301757991835)
(10.0, 0.7499979495399884)
(10.0, 0.7499979495399884)