Question

( underline{Q}=y=a sin (ln x) )
( begin{aligned} frac{d y}{d x} &=operatorname{acos}(ln x) cdot frac{1}{x}=frac{9}{x} cdot cos (ln x) frac{d^{2} y}{d x^{2}} &=frac{-a}{x^{2}} cos (ln x)+frac{a}{x} sin (ln x) cdot frac{1}{x} &=frac{-a}{x^{2}} cos left(ln (x)-frac{9}{x^{2}} sin (ln x)-(2)right.end{aligned} )
( Rightarrow ) multiply 0 by ( x^{prime} ) & (2) by ( x^{2}, ) woget
( x y_{1}=a cos (ln x) )
( x^{2} y_{2}=-a cos (ln x)-a sin (ln x) )
( y=a sin (ln x)-(6) )
Ad of ( (9+sqrt{5}+6), ) we get
( x^{2} y_{2}+x y_{1}+y=0 )

# y alin (loger) Prove that er yat ry, ty=0

Solution