Sr Examen
Ecuación diferencial dx*(x+sin(2*x)/y)+dy*(y-sin(x)^2/y^2)=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 d
sin (x)*--(y(x))
sin(2*x) d dx
x + -------- + --(y(x))*y(x) - ---------------- = 0
y(x) dx 2
y (x)
$$x + y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \frac{\sin{\left(2 x \right)}}{y{\left(x \right)}} - \frac{\sin^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)}}{y^{2}{\left(x \right)}} = 0$$
x + y*y' + sin(2*x)/y - sin(x)^2*y'/y^2 = 0
Respuesta
[src]
/ / 4 \ / 2 \\
| 3*|1 + --|*|-1 - --||
4 | 12 6 \ C1/ \ C1/|
2 / 2 \ x *|8 - --- - --- + --------------------|
x *|-1 - --| | 3 2 C1 |
\ C1/ \ C1 C1 / / 6\
y(x) = C1 + ------------ + ----------------------------------------- + O\x /
2*C1 2
24*C1
$$y{\left(x \right)} = \frac{x^{4} \left(8 + \frac{3 \left(-1 - \frac{2}{C_{1}}\right) \left(1 + \frac{4}{C_{1}}\right)}{C_{1}} - \frac{6}{C_{1}^{2}} - \frac{12}{C_{1}^{3}}\right)}{24 C_{1}^{2}} + \frac{x^{2} \left(-1 - \frac{2}{C_{1}}\right)}{2 C_{1}} + C_{1} + O\left(x^{6}\right)$$
Clasificación
factorable
1st exact
1st power series
lie group
1st exact Integral