Sr Examen
Ecuación diferencial ydx=(3x-y^2)dy
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2 d d
y(x) = - y (x)*--(y(x)) + 3*x*--(y(x))
dx dx
$$y{\left(x \right)} = 3 x \frac{d}{d x} y{\left(x \right)} - y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
y = 3*x*y' - y^2*y'
Respuesta
[src]
5 4 3 2
x 143*x 30*x 7*x 2*x / 6\
y(x) = C1 - -- - ------ - ----- - ---- - ---- + O\x /
C1 9 7 5 3
C1 C1 C1 C1
$$y{\left(x \right)} = - \frac{143 x^{5}}{C_{1}^{9}} - \frac{30 x^{4}}{C_{1}^{7}} - \frac{7 x^{3}}{C_{1}^{5}} - \frac{2 x^{2}}{C_{1}^{3}} - \frac{x}{C_{1}} + C_{1} + O\left(x^{6}\right)$$
Clasificación
factorable
1st exact
1st power series
lie group
1st exact Integral