Sr Examen
Ecuación diferencial 4(3x+y-2)dx−(3x+y)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d d
-8 + 4*y(x) + 12*x - --(y(x))*y(x) - 3*x*--(y(x)) = 0
dx dx
$$- 3 x \frac{d}{d x} y{\left(x \right)} + 12 x - y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 4 y{\left(x \right)} - 8 = 0$$
-3*x*y' + 12*x - y*y' + 4*y - 8 = 0
Respuesta
[src]
/ / / / 12\ \ \ / / 12\ \ \
| | | 8*|-7 + --| | | | 8*|-7 + --| | |
/ / / 12\ \ / 12\ \ | / 12\ | / 12\ | 144 \ C1/ / 2 \ / 16\| / / 12\ / 16\ \ / 16\ | | 144 \ C1/ / 2 \ / 16\| / / 12\ / 16\ \ / 16\ |
| | 8*|-7 + --| | 24*|-7 + --| | | 36*|-7 + --| | 12*|-7 + --| 2*|63 - --- + ----------- + 12*|1 - --|*|7 - --|| | 4*|-7 + --| 12*|7 - --| | 36*|7 - --| | 6*|63 - --- + ----------- + 12*|1 - --|*|7 - --|| | 4*|-7 + --| 12*|7 - --| | 108*|7 - --| |
2 / 8 \ 4 | 432 / 2 \ | 144 \ C1/ / 2 \ / 16\| \ C1/ / 2 \ / 16\| 3 / 36 / 2 \ / 12\\ 5 | 1620 \ C1/ / 2 \ | 540 \ C1/ \ C1 C1 \ C1/ \ C1// / 2 \ | 180 \ C1/ \ C1/ / 2 \ / 20\| \ C1/ / 2 \ / 20\| \ C1 C1 \ C1/ \ C1// / 2 \ | 180 \ C1/ \ C1/ / 2 \ / 20\| \ C1/ / 2 \ / 20\|
4*x *|7 - --| 2*x *|189 - --- + 4*|1 - --|*|63 - --- + ----------- + 12*|1 - --|*|7 - --|| + ------------ + 36*|1 - --|*|7 - --|| 8*x *|-21 + -- + 4*|1 - --|*|-7 + --|| 8*x *|-567 + ---- - ------------ + 4*|1 - --|*|-189 + --- - ------------ + ------------------------------------------------- + 4*|1 - --|*|-63 + --- - ----------- + ----------- + 12*|1 - --|*|-7 + --|| + ----------- + 36*|1 - --|*|-7 + --|| + ------------------------------------------------- + 12*|1 - --|*|-63 + --- - ----------- + ----------- + 12*|1 - --|*|-7 + --|| + ------------ + 108*|1 - --|*|-7 + --||
/ 2 \ \ C1/ \ C1 \ C1/ \ C1 C1 \ C1/ \ C1// C1 \ C1/ \ C1// \ C1 \ C1/ \ C1// \ C1 C1 \ C1/ \ C1 C1 C1 \ C1/ \ C1 C1 C1 \ C1/ \ C1// C1 \ C1/ \ C1// C1 \ C1/ \ C1 C1 C1 \ C1/ \ C1// C1 \ C1/ \ C1// / 6\
y(x) = C1 + 4*x*|1 - --| + ------------- + ------------------------------------------------------------------------------------------------------------------- + -------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + O\x /
\ C1/ 2 4 3 5
C1 3*C1 3*C1 15*C1
$$y{\left(x \right)} = \frac{8 x^{5} \left(108 \left(-7 + \frac{20}{C_{1}}\right) \left(1 - \frac{2}{C_{1}}\right) + 12 \left(1 - \frac{2}{C_{1}}\right) \left(12 \left(-7 + \frac{20}{C_{1}}\right) \left(1 - \frac{2}{C_{1}}\right) - 63 - \frac{4 \left(-7 + \frac{12}{C_{1}}\right)}{C_{1}} + \frac{12 \left(7 - \frac{16}{C_{1}}\right)}{C_{1}} + \frac{180}{C_{1}}\right) + 4 \left(1 - \frac{2}{C_{1}}\right) \left(36 \left(-7 + \frac{20}{C_{1}}\right) \left(1 - \frac{2}{C_{1}}\right) + 4 \left(1 - \frac{2}{C_{1}}\right) \left(12 \left(-7 + \frac{20}{C_{1}}\right) \left(1 - \frac{2}{C_{1}}\right) - 63 - \frac{4 \left(-7 + \frac{12}{C_{1}}\right)}{C_{1}} + \frac{12 \left(7 - \frac{16}{C_{1}}\right)}{C_{1}} + \frac{180}{C_{1}}\right) - 189 - \frac{12 \left(-7 + \frac{12}{C_{1}}\right)}{C_{1}} + \frac{36 \left(7 - \frac{16}{C_{1}}\right)}{C_{1}} + \frac{2 \left(12 \left(1 - \frac{2}{C_{1}}\right) \left(7 - \frac{16}{C_{1}}\right) + 63 + \frac{8 \left(-7 + \frac{12}{C_{1}}\right)}{C_{1}} - \frac{144}{C_{1}}\right)}{C_{1}} + \frac{540}{C_{1}}\right) - 567 - \frac{36 \left(-7 + \frac{12}{C_{1}}\right)}{C_{1}} + \frac{108 \left(7 - \frac{16}{C_{1}}\right)}{C_{1}} + \frac{6 \left(12 \left(1 - \frac{2}{C_{1}}\right) \left(7 - \frac{16}{C_{1}}\right) + 63 + \frac{8 \left(-7 + \frac{12}{C_{1}}\right)}{C_{1}} - \frac{144}{C_{1}}\right)}{C_{1}} + \frac{1620}{C_{1}}\right)}{15 C_{1}^{5}} + \frac{2 x^{4} \left(36 \left(1 - \frac{2}{C_{1}}\right) \left(7 - \frac{16}{C_{1}}\right) + 4 \left(1 - \frac{2}{C_{1}}\right) \left(12 \left(1 - \frac{2}{C_{1}}\right) \left(7 - \frac{16}{C_{1}}\right) + 63 + \frac{8 \left(-7 + \frac{12}{C_{1}}\right)}{C_{1}} - \frac{144}{C_{1}}\right) + 189 + \frac{24 \left(-7 + \frac{12}{C_{1}}\right)}{C_{1}} - \frac{432}{C_{1}}\right)}{3 C_{1}^{4}} + \frac{8 x^{3} \left(4 \left(-7 + \frac{12}{C_{1}}\right) \left(1 - \frac{2}{C_{1}}\right) - 21 + \frac{36}{C_{1}}\right)}{3 C_{1}^{3}} + \frac{4 x^{2} \left(7 - \frac{8}{C_{1}}\right)}{C_{1}^{2}} + 4 x \left(1 - \frac{2}{C_{1}}\right) + C_{1} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st power series
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 10.529103193459795)
(-5.555555555555555, 19.071150785497284)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 7.611001484716116e-42)
(7.777777777777779, 8.388243567338487e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)