We rescale the problem by putting
in our original differential equation
If
we get
The equation then transforms to
Consider the coefficients
The problem in the original equation is that the coefficient 
of the highest derivative y” is small compared to the others. To avoid this problem we thus choose the main coefficient
to be of the same order as one of the other coefficients and that the other two coefficients are comparably small. We demonstrate the procedure below (remember that is small):
| Case 1): |  |
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Case 2): |
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Case 3): |
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Ve see that we only have one possibility and that is Case 1, where the main coefficient is relatively larger than the remaining coefficients. We therefore choose
Our transformed equation then becomes
If we now put 
we get the equation
with the solution
The boundary condition z(0)=y(0)=0 then yields that
Our inner approximation is thus
The remaining problem is thus to determine the constant a and match the inner and outer approximations.