Sr Examen
Ecuación diferencial yy'=-x^2+y^2
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d 2 2 --(y(x))*y(x) = y (x) - x dx
$$y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = - x^{2} + y^{2}{\left(x \right)}$$
y*y' = -x^2 + y^2
Respuesta
[src]
__________________________
/ 2 2*x
-\/ 2 + 4*x + 4*x + C1*e
y(x) = -------------------------------
2
$$y{\left(x \right)} = - \frac{\sqrt{C_{1} e^{2 x} + 4 x^{2} + 4 x + 2}}{2}$$
__________________________
/ 2 2*x
\/ 2 + 4*x + 4*x + C1*e
y(x) = -----------------------------
2
$$y{\left(x \right)} = \frac{\sqrt{C_{1} e^{2 x} + 4 x^{2} + 4 x + 2}}{2}$$
Clasificación
almost linear
1st power series
lie group
almost linear Integral