Sr Examen
Ecuación diferencial xdy+(xy+2y-2^(-x))dx
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
-x d
- 2 + 2*y(x) + x*--(y(x)) + x*y(x) = 0
dx
$$x y{\left(x \right)} + x \frac{d}{d x} y{\left(x \right)} + 2 y{\left(x \right)} - 2^{- x} = 0$$
x*y + x*y' + 2*y - 2^(-x) = 0
Respuesta
[src]
x -x x 2 -x 1 + x -x
1 C1*2 *e C1*2 *log (2)*e C1*2 *e *log(2)
1 - - - log(2) + --------- + ----------------- - --------------------
x x x x
y(x) = ---------------------------------------------------------------------
/ x x 2 1 + x \
x*\2 + 2 *log (2) - 2 *log(2)/
$$y{\left(x \right)} = \frac{\frac{2^{x} C_{1} e^{- x} \log{\left(2 \right)}^{2}}{x} + \frac{2^{x} C_{1} e^{- x}}{x} - \frac{2^{x + 1} C_{1} e^{- x} \log{\left(2 \right)}}{x} - \log{\left(2 \right)} + 1 - \frac{1}{x}}{x \left(2^{x} \log{\left(2 \right)}^{2} + 2^{x} - 2^{x + 1} \log{\left(2 \right)}\right)}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st linear
Bernoulli
almost linear
lie group
1st exact Integral
1st linear Integral
Bernoulli Integral
almost linear Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -51.08245086092465)
(-5.555555555555555, -26.908272499478645)
(-3.333333333333333, -14.412037116683479)
(-1.1111111111111107, -19.96696445472504)
(1.1111111111111107, -7.57369621885359e+20)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 7.566503212566957e-67)
(7.777777777777779, 8.388243571829351e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)