Sr Examen
Ecuación diferencial tgx⋅y′′−y′+1sinx=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2
d d
- --(y(x)) + ---(y(x))*tan(x) + sin(x) = 0
dx 2
dx
$$\sin{\left(x \right)} + \tan{\left(x \right)} \frac{d^{2}}{d x^{2}} y{\left(x \right)} - \frac{d}{d x} y{\left(x \right)} = 0$$
sin(x) + tan(x)*y'' - y' = 0
Respuesta
[src]
/ 2/x\\ 2/x\ / 2/x\\ 2/x\ 2/x\ / /x\\
log|1 + tan |-|| tan |-|*log|1 + tan |-|| 2*tan |-|*log(2) 2*tan |-|*log|tan|-||
2 C2 \ \2// \2/ \ \2// \2/ \2/ \ \2//
y(x) = C1 - ----------- + ----------- - ---------------- + ------------------------ - ---------------- - ---------------------
2/x\ 2/x\ 2/x\ 2/x\ 2/x\ 2/x\
1 + tan |-| 1 + tan |-| 1 + tan |-| 1 + tan |-| 1 + tan |-| 1 + tan |-|
\2/ \2/ \2/ \2/ \2/ \2/
$$y{\left(x \right)} = C_{1} + \frac{C_{2}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2 \log{\left(2 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}$$
Clasificación
nth order reducible