Sr Examen
Ecuación diferencial ydx-4(xy+y^6)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
6 d d
- 4*y (x)*--(y(x)) - 4*x*--(y(x))*y(x) + y(x) = 0
dx dx
$$- 4 x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 4 y^{6}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} = 0$$
-4*x*y*y' - 4*y^6*y' + y = 0
Respuesta
[src]
y(x) = 0
$$y{\left(x \right)} = 0$$
/ / / 11\ / 3 \\ / 3 \ 2145 / 11\ \
| | 25*|8 + --| 55*|-2 - --|| 275*|-2 - --| 330 + ---- 75*|8 + --| |
| / 11\ / 3 \ / 3 \ / 15 15\ / 17\ / 11\ / 3 \ / 15 15\ | 15 15 \ C1/ \ C1/| 255 \ C1/ 4*C1 \ C1/ / 17\ / 11\ | / / / 11\ / 3 \\\
| 25*|8 + --| 55*|-2 - --| 55*|-2 - --| 5*|- -- - --| 15*|8 + --| 25*|8 + --| 55*|-2 - --| 5*|- -- - --| 5*|- -- - -- - ----------- + ------------| 120 + --- - ------------- + ---------- + ----------- 15*|8 + --| 25*|8 + --| | | | 25*|8 + --| 55*|-2 - --|||
| 15 15 15 15 \ C1/ \ C1/ 315 315 \ C1/ \ 2 C1/ \ C1/ \ C1/ 315 \ C1/ \ 2 C1/ \ 2 C1 64*C1 16*C1 / C1 8*C1 4*C1 32*C1 \ C1/ \ C1/ / 11\| / / 11\\ | / 11\ / 15 15\ | 15 15 \ C1/ \ C1/||
| - -- - -- - -- - -- - ----------- + ------------ 30 + ---- 30 + ---- - ------------ - ------------- + ----------- + ----------- 30 + ---- - ------------ - ------------- - ------------------------------------------ + ---------------------------------------------------- + ----------- + ----------- 5*|8 + --|| | 5*|8 + --|| | 5*|8 + --| 16*|- -- - --| 16*|- -- - -- - ----------- + ------------||
2 / 5 \ 5 | 75 2 C1 2 C1 64*C1 16*C1 4*C1 4*C1 16*C1 4*C1 4*C1 32*C1 4*C1 16*C1 4*C1 4*C1 4*C1 4*C1 32*C1 \ C1/| 3 | 60 \ C1/| 4 | 240 \ C1/ \ 2 C1/ \ 2 C1 64*C1 16*C1 /|
x *|-4 - --| x *|6 + ---- - --------- - -------------------------------------- + --------- + -------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ----------| x *|32 + -- + ----------| x *|-96 - --- - ---------- + -------------- + -------------------------------------------|
x \ C1/ \ 4*C1 2*C1 4*C1 4*C1 4*C1 4*C1 32*C1 / \ C1 C1 / \ C1 C1 C1 C1 / / 6\
y(x) = C1 + ----- + ------------ + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------- + ------------------------------------------------------------------------------------------ + O\x /
5 10 25 15 20
4*C1 32*C1 120*C1 384*C1 1536*C1
$$y{\left(x \right)} = \frac{x^{5} \left(6 - \frac{- \frac{15}{2} - \frac{15}{C_{1}}}{2 C_{1}} + \frac{5 \left(8 + \frac{11}{C_{1}}\right)}{32 C_{1}} + \frac{30 + \frac{315}{4 C_{1}}}{4 C_{1}} - \frac{- \frac{15}{2} + \frac{55 \left(-2 - \frac{3}{C_{1}}\right)}{16 C_{1}} - \frac{25 \left(8 + \frac{11}{C_{1}}\right)}{64 C_{1}} - \frac{15}{C_{1}}}{4 C_{1}} + \frac{30 - \frac{5 \left(- \frac{15}{2} - \frac{15}{C_{1}}\right)}{4 C_{1}} - \frac{55 \left(-2 - \frac{3}{C_{1}}\right)}{16 C_{1}} + \frac{25 \left(8 + \frac{11}{C_{1}}\right)}{32 C_{1}} + \frac{15 \left(8 + \frac{17}{C_{1}}\right)}{4 C_{1}} + \frac{315}{4 C_{1}}}{4 C_{1}} + \frac{30 - \frac{5 \left(- \frac{15}{2} - \frac{15}{C_{1}}\right)}{4 C_{1}} - \frac{55 \left(-2 - \frac{3}{C_{1}}\right)}{16 C_{1}} + \frac{25 \left(8 + \frac{11}{C_{1}}\right)}{32 C_{1}} + \frac{15 \left(8 + \frac{17}{C_{1}}\right)}{4 C_{1}} - \frac{5 \left(- \frac{15}{2} + \frac{55 \left(-2 - \frac{3}{C_{1}}\right)}{16 C_{1}} - \frac{25 \left(8 + \frac{11}{C_{1}}\right)}{64 C_{1}} - \frac{15}{C_{1}}\right)}{4 C_{1}} + \frac{120 - \frac{275 \left(-2 - \frac{3}{C_{1}}\right)}{8 C_{1}} + \frac{75 \left(8 + \frac{11}{C_{1}}\right)}{32 C_{1}} + \frac{330 + \frac{2145}{4 C_{1}}}{4 C_{1}} + \frac{255}{C_{1}}}{4 C_{1}} + \frac{315}{4 C_{1}}}{4 C_{1}} + \frac{75}{4 C_{1}}\right)}{120 C_{1}^{25}} + \frac{x^{4} \left(-96 + \frac{16 \left(- \frac{15}{2} - \frac{15}{C_{1}}\right)}{C_{1}} - \frac{5 \left(8 + \frac{11}{C_{1}}\right)}{C_{1}} + \frac{16 \left(- \frac{15}{2} + \frac{55 \left(-2 - \frac{3}{C_{1}}\right)}{16 C_{1}} - \frac{25 \left(8 + \frac{11}{C_{1}}\right)}{64 C_{1}} - \frac{15}{C_{1}}\right)}{C_{1}} - \frac{240}{C_{1}}\right)}{1536 C_{1}^{20}} + \frac{x^{3} \left(32 + \frac{5 \left(8 + \frac{11}{C_{1}}\right)}{C_{1}} + \frac{60}{C_{1}}\right)}{384 C_{1}^{15}} + \frac{x^{2} \left(-4 - \frac{5}{C_{1}}\right)}{32 C_{1}^{10}} + \frac{x}{4 C_{1}^{5}} + C_{1} + O\left(x^{6}\right)$$
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, 0.6857831711166421)
(-5.555555555555555, 0.6002335346491817)
(-3.333333333333333, 0.47119385607639985)
(-1.1111111111111107, 0.19581287689173163)
(1.1111111111111107, -1.1929468100959175)
(3.333333333333334, -1.453835955560697)
(5.555555555555557, -1.5953016195536425)
(7.777777777777779, -1.6963568667282867)
(10.0, -1.776218023806068)
(10.0, -1.776218023806068)