Sol=NDSolve[
y''[x]-3y'[x]+((5/(x^2))+Cos[x])y[x]==0&& y[1]==1 && y'[1]==0,
y[x], {x,ϵ=(10^(-9)),1}
];
Plot[Evaluate[y[x] /. Sol], {x,ϵ,1}, PlotPoints -> 1000]

LogLinearPlot[Evaluate[y[x] /. S], {x,ϵ,1}, PlotPoints -> 1000]

LogLogPlot[Evaluate[Abs[y[x]] /. S], {x,ϵ,1}, PlotPoints -> 1000]

Plot[(x^(1/10))Cos[Log[x]], {x, ϵ,1}, PlotPoints -> 1000]

LogLinearPlot[(x^3)Cos[Log[x]], {x, ϵ,1}, PlotPoints -> 1000]

NSolve[3r(r-1)+2r+3==0, r]

S=NDSolve[
y''[x]-8y'[x]+((10/(x^2))+Cos[x])y[x]==0&& y[1]==1 && y'[1]==0,
y[x], {x,ϵ=(10^(-15)),1}
];
Plot[Evaluate[y[x] /. S], {x,ϵ,1}, PlotPoints -> 1000]

LogLinearPlot[Evaluate[y[x] /. S], {x,ϵ,1}, PlotPoints -> 1000]