Sr Examen
Ecuación diferencial y''+sin(x)y'+cos(x)y=0
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Solución
Ha introducido
[src]
2
d d
--(y(x))*sin(x) + cos(x)*y(x) + ---(y(x)) = 0
dx 2
dx
$$y{\left(x \right)} \cos{\left(x \right)} + \sin{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \frac{d^{2}}{d x^{2}} y{\left(x \right)} = 0$$
y*cos(x) + sin(x)*y' + y'' = 0
Respuesta
[src]
/ 2 4 2 4 2 3 \ / 2 3 3 2 2 3 \
| x *cos(x) x *cos (x) x *sin (x)*cos(x) x *cos(x)*sin(x)| | x*sin(x) x *cos(x) x *sin (x) x *sin (x) x *cos(x)*sin(x)| / 6\
y(x) = C2*|1 - --------- + ---------- - ----------------- + ----------------| + C1*x*|1 - -------- - --------- - ---------- + ---------- + ----------------| + O\x /
\ 2 24 24 6 / \ 2 6 24 6 12 /
$$y{\left(x \right)} = C_{2} \left(- \frac{x^{4} \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{24} + \frac{x^{4} \cos^{2}{\left(x \right)}}{24} + \frac{x^{3} \sin{\left(x \right)} \cos{\left(x \right)}}{6} - \frac{x^{2} \cos{\left(x \right)}}{2} + 1\right) + C_{1} x \left(- \frac{x^{3} \sin^{3}{\left(x \right)}}{24} + \frac{x^{3} \sin{\left(x \right)} \cos{\left(x \right)}}{12} + \frac{x^{2} \sin^{2}{\left(x \right)}}{6} - \frac{x^{2} \cos{\left(x \right)}}{6} - \frac{x \sin{\left(x \right)}}{2} + 1\right) + O\left(x^{6}\right)$$
Clasificación
2nd power series ordinary