Sr Examen
Ecuación diferencial t^2*x''-2*t*x'+4*x=2*t*x
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Solución
Ha introducido
[src]
2
2 d d
4*x(t) + t *---(x(t)) - 2*t*--(x(t)) = 2*t*x(t)
2 dt
dt
$$t^{2} \frac{d^{2}}{d t^{2}} x{\left(t \right)} - 2 t \frac{d}{d t} x{\left(t \right)} + 4 x{\left(t \right)} = 2 t x{\left(t \right)}$$
t^2*x'' - 2*t*x' + 4*x = 2*t*x
Respuesta
[src]
3/2 / / ___ ___ ___\ / ___ ___ ___\\ x(t) = t *\C1*besselj\I*\/ 7 , 2*I*\/ 2 *\/ t / + C2*bessely\I*\/ 7 , 2*I*\/ 2 *\/ t //
$$x{\left(t \right)} = t^{\frac{3}{2}} \left(C_{1} J_{\sqrt{7} i}\left(2 \sqrt{2} i \sqrt{t}\right) + C_{2} Y_{\sqrt{7} i}\left(2 \sqrt{2} i \sqrt{t}\right)\right)$$
Clasificación
2nd linear bessel
2nd power series regular