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Question

Solve: t2d2xdt2+tdxdt+2y=0
t2d2ydt2+tdydt2x=0

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Solution

t2d2xdt2+tdxdt+2y=0

t2d2ydt2+tdydt2x=0

t2d2d+2(x+y)+tddt(x+y)

t2d2x+tdx+2y=0

t2d2y+tdy2x=0

(t2d2+dt)x+2y=0

(t2d2+td)y2x=0

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

d2t2(td+l)2y2x=0

d2t2(td+t)2+4y=0

(d2t2)(td+1)2+4]y=0

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