Sr Examen
Ecuación diferencial (3y-7x+7)dx-(3x-7y-3)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d d d
7 - 7*x + 3*--(y(x)) + 3*y(x) - 3*x*--(y(x)) + 7*--(y(x))*y(x) = 0
dx dx dx
$$- 3 x \frac{d}{d x} y{\left(x \right)} - 7 x + 7 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 3 y{\left(x \right)} + 3 \frac{d}{d x} y{\left(x \right)} + 7 = 0$$
-3*x*y' - 7*x + 7*y*y' + 3*y + 3*y' + 7 = 0
Respuesta
[src]
/ 5/7 2/7\
|/ -1 + x\ / -1 + x\ |
log(y(x)) = C1 - log||1 + ------| *|-1 + ------| |
\\ y(x) / \ y(x) / /
$$\log{\left(y{\left(x \right)} \right)} = C_{1} - \log{\left(\left(\frac{x - 1}{y{\left(x \right)}} - 1\right)^{\frac{2}{7}} \left(\frac{x - 1}{y{\left(x \right)}} + 1\right)^{\frac{5}{7}} \right)}$$
Clasificación
factorable
linear coefficients
1st power series
lie group
linear coefficients Integral