Sr Examen
Ecuación diferencial ydx+xdy=yarctgydy
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
d d x*--(y(x)) + y(x) = --(y(x))*atan(y(x))*y(x) dx dx
$$x \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} = y{\left(x \right)} \operatorname{atan}{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)}$$
x*y' + y = y*atan(y)*y'
Respuesta
[src]
2 y(x) atan(y(x)) y (x)*atan(y(x)) ---- - ---------- + x*y(x) - ---------------- = C1 2 2 2
$$x y{\left(x \right)} - \frac{y^{2}{\left(x \right)} \operatorname{atan}{\left(y{\left(x \right)} \right)}}{2} + \frac{y{\left(x \right)}}{2} - \frac{\operatorname{atan}{\left(y{\left(x \right)} \right)}}{2} = C_{1}$$
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, 0.9489554356649831)
(-5.555555555555555, 1.2739412606157086)
(-3.333333333333333, 1.8515840983656833)
(-1.1111111111111107, 2.9057894547681293)
(1.1111111111111107, 4.601211323660497)
(3.333333333333334, 6.806446604443149)
(5.555555555555557, 9.289523081184923)
(7.777777777777779, 11.910642515700722)
(10.0, 14.604160784113128)
(10.0, 14.604160784113128)