Sr Examen
Ecuación diferencial yy'+b(x-a)-(ay^2)/(1+x^2)=0
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Solución
Ha introducido
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2
d a*y (x)
b*(x - a) + --(y(x))*y(x) - ------- = 0
dx 2
1 + x
$$- \frac{a y^{2}{\left(x \right)}}{x^{2} + 1} + b \left(- a + x\right) + y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
-a*y^2/(x^2 + 1) + b*(-a + x) + y*y' = 0
Respuesta
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/ 2*a*atan(x) 2
y(x) = -\/ -b + C1*e - b*x
$$y{\left(x \right)} = - \sqrt{C_{1} e^{2 a \operatorname{atan}{\left(x \right)}} - b x^{2} - b}$$
_____________________________
/ 2*a*atan(x) 2
y(x) = \/ -b + C1*e - b*x
$$y{\left(x \right)} = \sqrt{C_{1} e^{2 a \operatorname{atan}{\left(x \right)}} - b x^{2} - b}$$
Clasificación
Bernoulli
almost linear
1st power series
lie group
Bernoulli Integral
almost linear Integral