Sr Examen
Ecuación diferencial y'+yx(y^6+1)dx+y^2(x^4+1)dy=0=7*e^x
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d
--(y(x))
7 dx 2 d 4 2 d
x*y (x) + x*y(x) + -------- + y (x)*--(y(x)) + x *y (x)*--(y(x)) = 0
dx dx dx
$$x^{4} y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + x y^{7}{\left(x \right)} + x y{\left(x \right)} + y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \frac{\frac{d}{d x} y{\left(x \right)}}{dx} = 0$$
x^4*y^2*y' + x*y^7 + x*y + y^2*y' + y'/dx = 0
Respuesta
[src]
/ 2 / 6\\
4 / 6\ | 6 2*C1 *\-1 - C1 /|
C1*x *\-1 - C1 /*|-1 - 7*C1 - ----------------|
| 2 1 |
2 / 6\ | C1 + -- |
C1*x *\-1 - C1 / \ dx / / 6\
y(x) = C1 + ---------------- + ------------------------------------------------ + O\x /
/ 2 1 \ 2
2*|C1 + --| / 2 1 \
\ dx/ 8*|C1 + --|
\ dx/
$$y{\left(x \right)} = C_{1} + \frac{C_{1} x^{2} \left(- C_{1}^{6} - 1\right)}{2 \left(C_{1}^{2} + \frac{1}{dx}\right)} + \frac{C_{1} x^{4} \left(- C_{1}^{6} - 1\right) \left(- 7 C_{1}^{6} - \frac{2 C_{1}^{2} \left(- C_{1}^{6} - 1\right)}{C_{1}^{2} + \frac{1}{dx}} - 1\right)}{8 \left(C_{1}^{2} + \frac{1}{dx}\right)^{2}} + O\left(x^{6}\right)$$
Clasificación
1st power series
lie group