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If y=acos(logx)+bsin(logx), prove that ...

If `y=acos(logx)+bsin(logx),` prove that ` x^2(d^2y)/(dx^2)+\ x(dy)/(dx)+y=0`

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`y = acos(logx)+bsin(logx)`
Let `logx = t =>1/xdx = dt=>dt/dx = 1/x`
Then, `y = acost+bsint`
`=>dy/dt = -asint+bcost`
`:.dy/dx = dy/dt*dt/dx = (-asint+bcost)1/x`
`=>xdy/dx = bcost-asint`
Differentiating w.r.t. `x`,
`=>x(d^2y)/dx^2+dy/dx = (-bsint-acost)dt/dx`
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