Sr Examen
Ecuación diferencial yy'=x√y²+1
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
d --(y(x))*y(x) = 1 + x*y(x) dx
$$y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = x y{\left(x \right)} + 1$$
y*y' = x*y + 1
Respuesta
[src]
/ / 15\\
| 7*|-4 + ---||
| | 3||
2 / 1 \ 3 / 3 \ 4 / 15\ 5 | 35 \ C1 /|
x *|1 - ---| x *|-1 + ---| x *|7 - ---| x *|6 - --- + ------------|
| 3| | 3| | 3| | 3 3 |
x \ C1 / \ C1 / \ C1 / \ C1 C1 / / 6\
y(x) = C1 + -- + ------------ + ------------- + ------------ + --------------------------- + O\x /
C1 2 2 4 3
6*C1 24*C1 120*C1
$$y{\left(x \right)} = \frac{x^{4} \left(7 - \frac{15}{C_{1}^{3}}\right)}{24 C_{1}^{4}} + \frac{x^{5} \left(6 + \frac{7 \left(-4 + \frac{15}{C_{1}^{3}}\right)}{C_{1}^{3}} - \frac{35}{C_{1}^{3}}\right)}{120 C_{1}^{3}} + \frac{x^{3} \left(-1 + \frac{3}{C_{1}^{3}}\right)}{6 C_{1}^{2}} + \frac{x}{C_{1}} + \frac{x^{2} \left(1 - \frac{1}{C_{1}^{3}}\right)}{2} + C_{1} + O\left(x^{6}\right)$$
Clasificación
1st power series
lie group