7. Use Taylor's series method to obtain the solution as a power series in \( x \) cupto the third derivative terms). given that \( \frac{d y}{d x}+y^{2}=x, y(0)=0 \). Using this generate the values of \( y \) corresponding to \( x=0.2,0.4,0.6 \) Correct to four decimal places. Then apply Milne's predictor-corrector formulae to compute \( y \) at \( x=0.8 \)

Question

7. Use Taylor's series method to obtain the solution as a power series in \( x \) cupto the third derivative terms). given that \( \frac{d y}{d x}+y^{2}=x, y(0)=0 \). Using this generate the values of \( y \) corresponding to \( x=0.2,0.4,0.6 \) Correct to four decimal places. Then apply Milne's predictor-corrector formulae to compute \( y \) at \( x=0.8 \)