Sr Examen
Ecuación diferencial dy/dx-2xy=x^2+y^2
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d 2 2
-2*x*y(x) + --(y(x)) = x + y (x)
dx
$$- 2 x y{\left(x \right)} + \frac{d}{d x} y{\left(x \right)} = x^{2} + y^{2}{\left(x \right)}$$
-2*x*y + y' = x^2 + y^2
Respuesta
[src]
3 / 2 2 / 2\\ 5 / 2 2 / 2\ 2 / 2 2 / 2\ 2 / 2\\ 2 / 2\\ 4 / 2 2 / 2\\
2 x *\1 + 3*C1 + C1 *\1 + 3*C1 // x *\2 + 9*C1 + C1 *\2 + 9*C1 / + C1 *\2 + 9*C1 + C1 *\2 + 9*C1 / + 2*C1 *\2 + 3*C1 // + 2*C1 *\2 + 3*C1 // 2 / 2\ C1*x *\2 + 3*C1 + C1 *\2 + 3*C1 // / 6\
y(x) = C1 + x*C1 + -------------------------------- + ------------------------------------------------------------------------------------------------------------ + C1*x *\1 + C1 / + ----------------------------------- + O\x /
3 15 3
$$y{\left(x \right)} = \frac{x^{3} \left(C_{1}^{2} \left(3 C_{1}^{2} + 1\right) + 3 C_{1}^{2} + 1\right)}{3} + \frac{x^{5} \left(2 C_{1}^{2} \left(3 C_{1}^{2} + 2\right) + C_{1}^{2} \left(9 C_{1}^{2} + 2\right) + C_{1}^{2} \left(2 C_{1}^{2} \left(3 C_{1}^{2} + 2\right) + C_{1}^{2} \left(9 C_{1}^{2} + 2\right) + 9 C_{1}^{2} + 2\right) + 9 C_{1}^{2} + 2\right)}{15} + C_{1} + C_{1} x^{2} \left(C_{1}^{2} + 1\right) + \frac{C_{1} x^{4} \left(C_{1}^{2} \left(3 C_{1}^{2} + 2\right) + 3 C_{1}^{2} + 2\right)}{3} + C_{1}^{2} x + O\left(x^{6}\right)$$
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, 8.726548494697138)
(-5.555555555555555, 414900995339.78455)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 6.971028255580836e+173)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 1.7159818507571235e+185)
(7.777777777777779, 8.388243567719543e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)