Sr Examen
Ecuación diferencial sinycosxdy=cosysinx
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Solución
Ha introducido
[src]
dy*cos(x)*sin(y(x)) = cos(y(x))*sin(x)
$$dy \sin{\left(y{\left(x \right)} \right)} \cos{\left(x \right)} = \sin{\left(x \right)} \cos{\left(y{\left(x \right)} \right)}$$
dy*sin(y)*cos(x) = sin(x)*cos(y)
Respuesta
[src]
/ _______________________________________________ \
| / 2 2/x\ 2 4/x\ 2 2/x\ 2/x\|
|-dy - / dy + 4*tan |-| + dy *tan |-| - 2*dy *tan |-| + dy*tan |-||
| \/ \2/ \2/ \2/ \2/|
y(x) = 2*atan|----------------------------------------------------------------------|
| /x\ |
| 2*tan|-| |
\ \2/ /
$$y{\left(x \right)} = 2 \operatorname{atan}{\left(\frac{dy \tan^{2}{\left(\frac{x}{2} \right)} - dy - \sqrt{dy^{2} \tan^{4}{\left(\frac{x}{2} \right)} - 2 dy^{2} \tan^{2}{\left(\frac{x}{2} \right)} + dy^{2} + 4 \tan^{2}{\left(\frac{x}{2} \right)}}}{2 \tan{\left(\frac{x}{2} \right)}} \right)}$$
/ _______________________________________________ \
| / 2 2/x\ 2 4/x\ 2 2/x\ 2/x\|
| / dy + 4*tan |-| + dy *tan |-| - 2*dy *tan |-| - dy + dy*tan |-||
|\/ \2/ \2/ \2/ \2/|
y(x) = 2*atan|---------------------------------------------------------------------|
| /x\ |
| 2*tan|-| |
\ \2/ /
$$y{\left(x \right)} = 2 \operatorname{atan}{\left(\frac{dy \tan^{2}{\left(\frac{x}{2} \right)} - dy + \sqrt{dy^{2} \tan^{4}{\left(\frac{x}{2} \right)} - 2 dy^{2} \tan^{2}{\left(\frac{x}{2} \right)} + dy^{2} + 4 \tan^{2}{\left(\frac{x}{2} \right)}}}{2 \tan{\left(\frac{x}{2} \right)}} \right)}$$
Clasificación
nth algebraic
nth algebraic Integral