Question

Solve: $t^2\frac{d^{2}x}{d{t}^2}+t\frac{dx}{dt}+2y=0$
$t^2\frac{d^{2}y}{d{t}^2}+t\frac{dy}{dt}-2x=0$

Answer 1

$t^2\frac{d^{2}x}{d{t}^2}+t\frac{dx}{dt}+2y=0$

$t^2\frac{d^{2}y}{d{t}^2}+t\frac{dy}{dt}-2x=0$

$t^2\frac{d^2}{d+2}(x+y)+t\frac{d}{dt}(x+y)-$

$t^2{d}^{2}x+tdx+2y=0$

$t^2{d}^{2}y+tdy-2x=0$

$(t^2{d}^2+dt)x+2y=0$

$(t^2{d}^2+td)y-2x=0$

$2d+(td+l)x+4x=0$

$d^2{t}^2(td+l{)}^{2}y-2x=0$

$d^2{t}^2(td+t{)}^2+4y=0$

$\left(d^2{t}^2\right)(td+1{)}^2+4]y=0$