Sr Examen
Ecuación diferencial (ln(y)-5*y^2*sin5x)dx+(x/y+2*y*cos5x)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d
x*--(y(x))
2 dx d
- 5*y (x)*sin(5*x) + ---------- + 2*--(y(x))*cos(5*x)*y(x) + log(y(x)) = 0
y(x) dx
$$\frac{x \frac{d}{d x} y{\left(x \right)}}{y{\left(x \right)}} - 5 y^{2}{\left(x \right)} \sin{\left(5 x \right)} + 2 y{\left(x \right)} \cos{\left(5 x \right)} \frac{d}{d x} y{\left(x \right)} + \log{\left(y{\left(x \right)} \right)} = 0$$
x*y'/y - 5*y^2*sin(5*x) + 2*y*cos(5*x)*y' + log(y) = 0
Respuesta
[src]
/ 2*C1 2*C1 \
| -5*I*x + ---- ---- + 5*I*x|
| x x |
|e + e |
W|------------------------------|
\ x / C1
- --------------------------------- + --
2 x
y(x) = e
$$y{\left(x \right)} = e^{\frac{C_{1}}{x} - \frac{W\left(\frac{e^{\frac{2 C_{1}}{x} - 5 i x} + e^{\frac{2 C_{1}}{x} + 5 i x}}{x}\right)}{2}}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.6577162941052498)
(-5.555555555555555, 0.5178974166198758)
(-3.333333333333333, 0.3509494309409326)
(-1.1111111111111107, 0.04613345552253436)
(1.1111111111111107, nan)
(3.333333333333334, nan)
(5.555555555555557, nan)
(7.777777777777779, nan)
(10.0, nan)
(10.0, nan)