Sr Examen
Ecuación diferencial (10xy-8y+1)dx+(5x^2-8x+3)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d d 2 d
1 - 8*y(x) + 3*--(y(x)) - 8*x*--(y(x)) + 5*x *--(y(x)) + 10*x*y(x) = 0
dx dx dx
$$5 x^{2} \frac{d}{d x} y{\left(x \right)} + 10 x y{\left(x \right)} - 8 x \frac{d}{d x} y{\left(x \right)} - 8 y{\left(x \right)} + 3 \frac{d}{d x} y{\left(x \right)} + 1 = 0$$
5*x^2*y' + 10*x*y - 8*x*y' - 8*y + 3*y' + 1 = 0
Respuesta
[src]
C1 - x
y(x) = --------------
2
3 - 8*x + 5*x
$$y{\left(x \right)} = \frac{C_{1} - x}{5 x^{2} - 8 x + 3}$$
Clasificación
1st exact
1st linear
Bernoulli
almost linear
1st power series
lie group
1st exact Integral
1st linear Integral
Bernoulli Integral
almost linear Integral