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