Sr Examen
Ecuación diferencial y'=(3x+3y-1)/2(x+y)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
d / 1 3*x 3*y(x)\ --(y(x)) = (x + y(x))*|- - + --- + ------| dx \ 2 2 2 /
$$\frac{d}{d x} y{\left(x \right)} = \left(x + y{\left(x \right)}\right) \left(\frac{3 x}{2} + \frac{3 y{\left(x \right)}}{2} - \frac{1}{2}\right)$$
y' = (x + y)*(3*x/2 + 3*y/2 - 1/2)
Respuesta
[src]
/ / 2\\ / / / 2\ \\ / / / / 2\ \ / 2 2 \\\
| | 2 3*C1 9*C1 || | | 9 | 2 3*C1 9*C1 | C1*(-1 + 3*C1)*(-9/2 + 27*C1)|| | | 2 2 | 9 | 2 3*C1 9*C1 | C1*(-1 + 3*C1)*(-9/2 + 27*C1)| C1*(-1 + 3*C1)*\36 - 18*C1 + 3*(-1/2 + 3*C1) + 54*C1 + 2*(-9/2 + 27*C1)*(-1/2 + 3*C1)/||
| 2 C1*(-1 + 3*C1)*|3 + (-1/2 + 3*C1) - ---- + -----|| | / 2\ C1*(-1 + 3*C1)*|- - + 27*C1 + (-1/2 + 3*C1)*|3 + (-1/2 + 3*C1) - ---- + -----| + -----------------------------|| | / / 2\ \ / 2 2 \ C1*(-1 + 3*C1)*|36 - 18*C1 + 3*(-1/2 + 3*C1) + 54*C1 + (-1/2 + 3*C1)*|- - + 27*C1 + (-1/2 + 3*C1)*|3 + (-1/2 + 3*C1) - ---- + -----| + -----------------------------| + 2*(-9/2 + 27*C1)*(-1/2 + 3*C1) + ----------------------------------------------------------------------------------------||
2 / 1 C1*(-1 + 3*C1)*(-1/2 + 3*C1)\ 3 | 2 3*C1 9*C1 \ 2 2 /| 4 | 9 | 2 3*C1 9*C1 | C1*(-1 + 3*C1)*(-9/2 + 27*C1) \ 2 \ 2 2 / 2 /| 5 | 2 2 | 9 | 2 3*C1 9*C1 | C1*(-1 + 3*C1)*(-9/2 + 27*C1)| C1*(-1 + 3*C1)*\36 - 18*C1 + 3*(-1/2 + 3*C1) + 54*C1 + 2*(-9/2 + 27*C1)*(-1/2 + 3*C1)/ \ \ 2 \ 2 2 / 2 / 2 /|
x *|- - + 3*C1 + ----------------------------| x *|3 + (-1/2 + 3*C1) - ---- + ----- + --------------------------------------------------| x *|- - + 27*C1 + (-1/2 + 3*C1)*|3 + (-1/2 + 3*C1) - ---- + -----| + ----------------------------- + ----------------------------------------------------------------------------------------------------------------| x *|36 - 18*C1 + 3*(-1/2 + 3*C1) + 54*C1 + (-1/2 + 3*C1)*|- - + 27*C1 + (-1/2 + 3*C1)*|3 + (-1/2 + 3*C1) - ---- + -----| + -----------------------------| + 2*(-9/2 + 27*C1)*(-1/2 + 3*C1) + ---------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\ 2 2 / \ 2 2 2 / \ 2 \ 2 2 / 2 2 / \ \ 2 \ 2 2 / 2 / 2 2 / C1*x*(-1 + 3*C1) / 6\
y(x) = C1 + ---------------------------------------------- + ------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------- + O\x /
2 6 24 120 2
$$y{\left(x \right)} = \frac{x^{2} \left(\frac{C_{1} \left(3 C_{1} - 1\right) \left(3 C_{1} - \frac{1}{2}\right)}{2} + 3 C_{1} - \frac{1}{2}\right)}{2} + \frac{x^{3} \left(\frac{9 C_{1}^{2}}{2} + \frac{C_{1} \left(3 C_{1} - 1\right) \left(\frac{9 C_{1}^{2}}{2} - \frac{3 C_{1}}{2} + \left(3 C_{1} - \frac{1}{2}\right)^{2} + 3\right)}{2} - \frac{3 C_{1}}{2} + \left(3 C_{1} - \frac{1}{2}\right)^{2} + 3\right)}{6} + \frac{x^{4} \left(\frac{C_{1} \left(3 C_{1} - 1\right) \left(27 C_{1} - \frac{9}{2}\right)}{2} + \frac{C_{1} \left(3 C_{1} - 1\right) \left(\frac{C_{1} \left(3 C_{1} - 1\right) \left(27 C_{1} - \frac{9}{2}\right)}{2} + 27 C_{1} + \left(3 C_{1} - \frac{1}{2}\right) \left(\frac{9 C_{1}^{2}}{2} - \frac{3 C_{1}}{2} + \left(3 C_{1} - \frac{1}{2}\right)^{2} + 3\right) - \frac{9}{2}\right)}{2} + 27 C_{1} + \left(3 C_{1} - \frac{1}{2}\right) \left(\frac{9 C_{1}^{2}}{2} - \frac{3 C_{1}}{2} + \left(3 C_{1} - \frac{1}{2}\right)^{2} + 3\right) - \frac{9}{2}\right)}{24} + \frac{x^{5} \left(54 C_{1}^{2} + \frac{C_{1} \left(3 C_{1} - 1\right) \left(54 C_{1}^{2} - 18 C_{1} + 3 \left(3 C_{1} - \frac{1}{2}\right)^{2} + 2 \left(3 C_{1} - \frac{1}{2}\right) \left(27 C_{1} - \frac{9}{2}\right) + 36\right)}{2} + \frac{C_{1} \left(3 C_{1} - 1\right) \left(54 C_{1}^{2} + \frac{C_{1} \left(3 C_{1} - 1\right) \left(54 C_{1}^{2} - 18 C_{1} + 3 \left(3 C_{1} - \frac{1}{2}\right)^{2} + 2 \left(3 C_{1} - \frac{1}{2}\right) \left(27 C_{1} - \frac{9}{2}\right) + 36\right)}{2} - 18 C_{1} + 3 \left(3 C_{1} - \frac{1}{2}\right)^{2} + 2 \left(3 C_{1} - \frac{1}{2}\right) \left(27 C_{1} - \frac{9}{2}\right) + \left(3 C_{1} - \frac{1}{2}\right) \left(\frac{C_{1} \left(3 C_{1} - 1\right) \left(27 C_{1} - \frac{9}{2}\right)}{2} + 27 C_{1} + \left(3 C_{1} - \frac{1}{2}\right) \left(\frac{9 C_{1}^{2}}{2} - \frac{3 C_{1}}{2} + \left(3 C_{1} - \frac{1}{2}\right)^{2} + 3\right) - \frac{9}{2}\right) + 36\right)}{2} - 18 C_{1} + 3 \left(3 C_{1} - \frac{1}{2}\right)^{2} + 2 \left(3 C_{1} - \frac{1}{2}\right) \left(27 C_{1} - \frac{9}{2}\right) + \left(3 C_{1} - \frac{1}{2}\right) \left(\frac{C_{1} \left(3 C_{1} - 1\right) \left(27 C_{1} - \frac{9}{2}\right)}{2} + 27 C_{1} + \left(3 C_{1} - \frac{1}{2}\right) \left(\frac{9 C_{1}^{2}}{2} - \frac{3 C_{1}}{2} + \left(3 C_{1} - \frac{1}{2}\right)^{2} + 3\right) - \frac{9}{2}\right) + 36\right)}{120} + C_{1} + \frac{C_{1} x \left(3 C_{1} - 1\right)}{2} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
1st power series
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 9.87488550730535)
(-5.555555555555555, 4341592027.48288)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 3.94276075276142e-62)
(7.777777777777779, 8.388243567718792e+296)
(10.0, 9.036991477623112e-277)
(10.0, 9.036991477623112e-277)