Sr Examen
Ecuación diferencial 3*x*y'-y(1+x*sin(x)-3*y^3*sin(x))=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
/ 3 \ d
- \1 + x*sin(x) - 3*y (x)*sin(x)/*y(x) + 3*x*--(y(x)) = 0
dx
$$3 x \frac{d}{d x} y{\left(x \right)} - \left(x \sin{\left(x \right)} - 3 y^{3}{\left(x \right)} \sin{\left(x \right)} + 1\right) y{\left(x \right)} = 0$$
3*x*y' - (x*sin(x) - 3*y^3*sin(x) + 1)*y = 0
Respuesta
[src]
________________
/ x
y(x) = / --------------
3 / cos(x)
\/ 3 + C1*e
$$y{\left(x \right)} = \sqrt[3]{\frac{x}{C_{1} e^{\cos{\left(x \right)}} + 3}}$$
________________
/ x / 2/3 6 ___\
/ -------------- *\- 3 - 3*I*\/ 3 /
3 / cos(x)
\/ 1 + C1*e
y(x) = ------------------------------------------
6
$$y{\left(x \right)} = \frac{\sqrt[3]{\frac{x}{C_{1} e^{\cos{\left(x \right)}} + 1}} \left(- 3^{\frac{2}{3}} - 3 \sqrt[6]{3} i\right)}{6}$$
________________
/ x / 2/3 6 ___\
/ -------------- *\- 3 + 3*I*\/ 3 /
3 / cos(x)
\/ 1 + C1*e
y(x) = ------------------------------------------
6
$$y{\left(x \right)} = \frac{\sqrt[3]{\frac{x}{C_{1} e^{\cos{\left(x \right)}} + 1}} \left(- 3^{\frac{2}{3}} + 3 \sqrt[6]{3} i\right)}{6}$$
Gráfico para el problema de Cauchy
Clasificación
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.4961379717081178)
(-5.555555555555555, 0.3519786708647037)
(-3.333333333333333, 0.548909064064217)
(-1.1111111111111107, 0.22835712169433198)
(1.1111111111111107, 0.03409167809497919)
(3.333333333333334, 6.95183464922136e-310)
(5.555555555555557, 6.95183464756604e-310)
(7.777777777777779, 6.9520529151772e-310)
(10.0, 6.9518346493257e-310)
(10.0, 6.9518346493257e-310)