Sr Examen
Ecuación diferencial x^2dy^2/dx^2-3xdy/dx+5y=x^2sin(log(x))
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2
2 d d 2
5*y(x) + x *---(y(x)) - 3*x*--(y(x)) = x *sin(log(x))
2 dx
dx
$$x^{2} \frac{d^{2}}{d x^{2}} y{\left(x \right)} - 3 x \frac{d}{d x} y{\left(x \right)} + 5 y{\left(x \right)} = x^{2} \sin{\left(\log{\left(x \right)} \right)}$$
x^2*y'' - 3*x*y' + 5*y = x^2*sin(log(x))
Respuesta
[src]
2 / cos(log(x))*log(x)\
y(x) = x *|C1*sin(log(x)) + C2*cos(log(x)) - ------------------|
\ 2 /
$$y{\left(x \right)} = x^{2} \left(C_{1} \sin{\left(\log{\left(x \right)} \right)} + C_{2} \cos{\left(\log{\left(x \right)} \right)} - \frac{\log{\left(x \right)} \cos{\left(\log{\left(x \right)} \right)}}{2}\right)$$
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