Answer to Question #318209 in Calculus for I AM LEGEND

Question

Find the Frobenius series solution of the differential equation 3x(d²y/dx²) −[(1−x)dy/dx]− y = 0. Hence, show that if y(0)=0, then

y = Ax^(4/3) [1−(x/21)+ (x²/315)−....] is the solution where A is an arbitrary constant.