Sr Examen
Ecuación diferencial x^2y''-3xy'+3y=3ln^2x
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2
2 d d 2
3*y(x) + x *---(y(x)) - 3*x*--(y(x)) = 3*log (x)
2 dx
dx
$$x^{2} \frac{d^{2}}{d x^{2}} y{\left(x \right)} - 3 x \frac{d}{d x} y{\left(x \right)} + 3 y{\left(x \right)} = 3 \log{\left(x \right)}^{2}$$
x^2*y'' - 3*x*y' + 3*y = 3*log(x)^2
Respuesta
[src]
26 2 8*log(x) 3
y(x) = -- + log (x) + -------- + C1*x + C2*x
9 3
$$y{\left(x \right)} = C_{1} x + C_{2} x^{3} + \log{\left(x \right)}^{2} + \frac{8 \log{\left(x \right)}}{3} + \frac{26}{9}$$
Clasificación
nth linear euler eq nonhomogeneous undetermined coefficients
nth linear euler eq nonhomogeneous variation of parameters
nth linear euler eq nonhomogeneous variation of parameters Integral