\(y'-3x^2y= e^(x^3)\)

\(\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}-{3}{x}^{2}{y}={e}^{{{x}^{3}}}\)

\(\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}+{P}{y}={Q}\)

\(P= -3x^2\), \(\displaystyle{Q}={e}^{{{x}^{3}}}\)

\(\displaystyle{I}.{F}.={e}^{{\int{P}{\left.{d}{x}\right.}}}\)

\(\displaystyle={e}^{{\int-{3}\frac{{x}^{3}}{{3}}}}\)

\(\displaystyle={e}^{{-{x}^{3}}}\)

\(\displaystyle=\frac{1}{{e}^{{{x}^{3}}}}\)

\(\displaystyle{y}{\left({I}.{F}.\right)}=\int{Q}{\left({I}.{F}.\right)}{\left.{d}{x}\right.}+{C}\)

\(\displaystyle{y}\frac{1}{{e}^{{{x}^{3}}}}=\int{e}^{{{x}^{3}}}\frac{1}{{e}^{{{x}^{3}}}}{\left.{d}{x}\right.}+{C}\)