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Ecuaciones diferenciales/
y''(x)*x^2*sin(x)-x*(2*sin(x)+x*cos(x))*y'(x)+(2*sin(x)+x*cos(x))*y(x)=-x^4*(sin(x))^2
Ecuación diferencial y''(x)*x^2*sin(x)-x*(2*sin(x)+x*cos(x))*y'(x)+(2*sin(x)+x*cos(x))*y(x)=-x^4*(sin(x))^2
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2
3 d 2 d 4 2
x*(2*sin(x) + x*cos(x))*y(x) + x *---(y(x))*sin(x) - x *(2*sin(x) + x*cos(x))*--(y(x)) = -x *sin (x)
2 dx
dx
$$x^{3} \sin{\left(x \right)} \frac{d^{2}}{d x^{2}} y{\left(x \right)} - x^{2} \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \frac{d}{d x} y{\left(x \right)} + x \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) y{\left(x \right)} = - x^{4} \sin^{2}{\left(x \right)}$$
x^3*sin(x)*y'' - x^2*(x*cos(x) + 2*sin(x))*y' + x*(x*cos(x) + 2*sin(x))*y = -x^4*sin(x)^2
Clasificación
factorable