Sr Examen
Ecuación diferencial y''+2*(tanx)*y'+(1+(e^x+e^(-x))/2)*y=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
/ x -x\ 2
| e e | d d
|1 + -- + ---|*y(x) + 2*--(y(x))*tan(x) + ---(y(x)) = 0
\ 2 2 / dx 2
dx
$$\left(\frac{e^{x}}{2} + 1 + \frac{e^{- x}}{2}\right) y{\left(x \right)} + 2 \tan{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = 0$$
(exp(x)/2 + 1 + exp(-x)/2)*y + 2*tan(x)*y' + y'' = 0
Respuesta
[src]
/ 2 4 2 x 2 -x 4 2 3 4 x 4 -x 4 -2*x 4 2*x 4 2 x 4 2 -x 3 x 3 -x \ / 2 3 3 2 x 2 -x 3 2 2 3 x 3 -x \
| x x x *e x *e x *tan (x) x *tan(x) x *e x *e x *e x *e x *tan (x)*e x *tan (x)*e x *e *tan(x) x *e *tan(x)| | x x *tan (x) x *e x *e x *tan(x) 2*x *tan (x) x *e *tan(x) x *e *tan(x)| / 6\
y(x) = C2*|1 - -- + -- - ----- - ------ - ---------- + --------- + ----- + ------ + -------- + ------- - ------------- - -------------- + ------------ + -------------| + C1*x*|1 - -- - x*tan(x) - ---------- - ----- - ------ + --------- + ------------ + ------------ + -------------| + O\x /
\ 2 16 4 4 6 3 24 24 96 96 12 12 6 6 / \ 6 3 12 12 6 3 12 12 /
$$y{\left(x \right)} = C_{2} \left(\frac{x^{4} e^{2 x}}{96} - \frac{x^{4} e^{x} \tan^{2}{\left(x \right)}}{12} + \frac{x^{4} e^{x}}{24} - \frac{x^{4} \tan^{2}{\left(x \right)}}{6} + \frac{x^{4}}{16} - \frac{x^{4} e^{- x} \tan^{2}{\left(x \right)}}{12} + \frac{x^{4} e^{- x}}{24} + \frac{x^{4} e^{- 2 x}}{96} + \frac{x^{3} e^{x} \tan{\left(x \right)}}{6} + \frac{x^{3} \tan{\left(x \right)}}{3} + \frac{x^{3} e^{- x} \tan{\left(x \right)}}{6} - \frac{x^{2} e^{x}}{4} - \frac{x^{2}}{2} - \frac{x^{2} e^{- x}}{4} + 1\right) + C_{1} x \left(\frac{x^{3} e^{x} \tan{\left(x \right)}}{12} - \frac{x^{3} \tan^{3}{\left(x \right)}}{3} + \frac{x^{3} \tan{\left(x \right)}}{6} + \frac{x^{3} e^{- x} \tan{\left(x \right)}}{12} - \frac{x^{2} e^{x}}{12} + \frac{2 x^{2} \tan^{2}{\left(x \right)}}{3} - \frac{x^{2}}{6} - \frac{x^{2} e^{- x}}{12} - x \tan{\left(x \right)} + 1\right) + O\left(x^{6}\right)$$
Clasificación
2nd power series ordinary