यदि `y=3 cos(log g)+4 sin ( log x)` तो सिद्ध कीजिये की `x^(2)y_(2)+xy_(1)+y=0`

Explanation

`y=3cos(logx)+4sin (logx) ` ...(1)
`rArr y_(1)=-3sin (log x ). (1)/(x) + 4 cos (log x ) . (1)/(x)`
`rArr xy_(1)=-3sin (log x ) + 4 cos (log x)`
`rArr xy_(2)+y_(1)=-3cos (logx).(1)/(x)-4sin (log x) . (1)/(x)`
`rArr x^(2)y_(2)+xy_(1)=-3cos(logx)-4sin (logx)`
`=-[3cos (log x) + 4 sin ( log x)]`
`=-y`
`rArr x^(2)y_(2)+xy_(1)+y=0`. ( इति सिध्दम )