Sr Examen
Ecuación diferencial tsin(t)dx+(tcos(t)+sin(t))xdt=sin(t)dt
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d
sin(t)*x(t) + t*--(x(t))*sin(t) + t*cos(t)*x(t) = sin(t)
dt
$$t x{\left(t \right)} \cos{\left(t \right)} + t \sin{\left(t \right)} \frac{d}{d t} x{\left(t \right)} + x{\left(t \right)} \sin{\left(t \right)} = \sin{\left(t \right)}$$
t*x*cos(t) + t*sin(t)*x' + x*sin(t) = sin(t)
Respuesta
[src]
_________
/ 1
-1 + C1* / -------
/ 2
\/ cos (t)
x(t) = ----------------------
t*tan(t)
$$x{\left(t \right)} = \frac{C_{1} \sqrt{\frac{1}{\cos^{2}{\left(t \right)}}} - 1}{t \tan{\left(t \right)}}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st exact
1st linear
Bernoulli
almost linear
lie group
1st exact Integral
1st linear Integral
Bernoulli Integral
almost linear Integral
Respuesta numérica
[src]
(t, x):
(-10.0, 0.75)
(-7.777777777777778, 3395173.669512968)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 6.971028255580836e+173)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 2.125757255287192e+160)
(7.777777777777779, 8.388243571811803e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)