I need to solve the differential equation
DSolve[{(1-x)y''[x]==1/5 \[Sqrt](1+y'[x]^2),y[0]==0,y'[0]==0},y[x],x]
but the result given seems to be incorrect and returns an error "Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information". How to solve? The correct solution should be
How to solve it correctly?
Rationalize[N[y[x]/.DSolve[...]]]
and decide whether "the result given seems to be incorrect." As always with Mathematica, there are probably half a dozen other ways of doing anything and there may be a better way of doing that. Also, errors are very different from warnings, but a new user may not be able to tell the difference. $\endgroup$