Consider a differential equation zy" + (1 + x)y' + y =0.y(0) = 1,y(1) = 1. Prove that 6 1 1 72(x) = (1 + x)$ 2(1 + x)3 4(1 + x) for the outer solution and, Y (X)= -X+ An NIE X -* +X+ A(e-*-1). and Y2(X) = X2 -2X+ Ag -x - X" + 2X )+ A(- NIH X' e-* + X + Az(e-* - 1). 8 for the inner solution