Sr Examen
Ecuación diferencial dx*(x*log(y)+y)+dy*(x^2/(2*y)+x+1)=0
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Solución
Ha introducido
[src]
2 d
x *--(y(x))
d dx d
x*--(y(x)) + x*log(y(x)) + ----------- + --(y(x)) + y(x) = 0
dx 2*y(x) dx
$$\frac{x^{2} \frac{d}{d x} y{\left(x \right)}}{2 y{\left(x \right)}} + x \log{\left(y{\left(x \right)} \right)} + x \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} + \frac{d}{d x} y{\left(x \right)} = 0$$
x^2*y'/(2*y) + x*log(y) + x*y' + y + y' = 0
Respuesta
[src]
/ C1\
| --|
| 2|
| x |
2 |2*(1 + x)*e |
x *W|-------------|
| 2 |
\ x /
y(x) = -------------------
2*(1 + x)
$$y{\left(x \right)} = \frac{x^{2} W\left(\frac{2 \left(x + 1\right) e^{\frac{C_{1}}{x^{2}}}}{x^{2}}\right)}{2 \left(x + 1\right)}$$
Clasificación
1st exact
1st power series
lie group
1st exact Integral