Sr Examen
Ecuación diferencial xy''+y'=y'*ln(y'/x)
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Solución
Ha introducido
[src]
/d \
2 |--(y(x))|
d d d |dx |
x*---(y(x)) + --(y(x)) = --(y(x))*log|--------|
2 dx dx \ x /
dx
$$x \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d}{d x} y{\left(x \right)} = \log{\left(\frac{\frac{d}{d x} y{\left(x \right)}}{x} \right)} \frac{d}{d x} y{\left(x \right)}$$
x*y'' + y' = log(y'/x)*y'
Respuesta
[src]
// 2 + C1*x \
||(-1 + C1*x)*e 2 |
||--------------------- for C1 != 0|
|| 2 |
|| C1 |
y(x) = C1 + |< |
|| 2 |
|| x |
|| -- otherwise |
|| 2 |
\\ /
$$y{\left(x \right)} = C_{1} + \begin{cases} \frac{\left(C_{1} x - 1\right) e^{C_{1} x + 2}}{C_{1}^{2}} & \text{for}\: C_{1}^{2} \neq 0 \\\frac{x^{2}}{2} & \text{otherwise} \end{cases}$$
Clasificación
nth order reducible