Sr Examen
Ecuación diferencial y'+2x*1-y^2=y^1(1+x^2)y=7*e^x
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Solución
Ha introducido
[src]
2 d 2 / 2\
- y (x) + 2*x + --(y(x)) = y (x)*\1 + x /
dx
$$2 x - y^{2}{\left(x \right)} + \frac{d}{d x} y{\left(x \right)} = \left(x^{2} + 1\right) y^{2}{\left(x \right)}$$
2*x - y^2 + y' = (x^2 + 1)*y^2
Respuesta
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5 / 3 4 3 3 / 3 / 2\\\ 3 / 3\ 2 4 / 3\
2 / 3\ 2 2*x *\3 - 24*C1 - 3*C1 + 9*C1 + C1 *(-16 + 9*C1) + C1 *\-20 + 11*C1 + 96*C1 + C1*\1 + 144*C1 /// C1*x *\-4 + C1 + 24*C1 / 2*C1 *x *\-5 + 2*C1 + 24*C1 / / 6\
y(x) = C1 + x *\-1 + 4*C1 / + 2*x*C1 + --------------------------------------------------------------------------------------------------- + ------------------------ + ----------------------------- + O\x /
15 3 3
$$y{\left(x \right)} = x^{2} \left(4 C_{1}^{3} - 1\right) + \frac{2 x^{5} \left(9 C_{1}^{4} + C_{1}^{3} \left(9 C_{1} - 16\right) + C_{1}^{3} \left(96 C_{1}^{3} + C_{1} \left(144 C_{1}^{2} + 1\right) + 11 C_{1} - 20\right) - 24 C_{1}^{3} - 3 C_{1} + 3\right)}{15} + C_{1} + \frac{C_{1} x^{3} \left(24 C_{1}^{3} + C_{1} - 4\right)}{3} + 2 C_{1}^{2} x + \frac{2 C_{1}^{2} x^{4} \left(24 C_{1}^{3} + 2 C_{1} - 5\right)}{3} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
1st power series
lie group
Respuesta numérica
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(x, y):
(-10.0, 0.75)
(-7.777777777777778, 732460831.5163392)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 6.397106897951207e+170)
(7.777777777777779, 8.38824356695602e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)