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