# Solve differential equationy'-3x^2y= e^(x^3)

Solve differential equation $$\displaystyle{y}'-{3}{x}^{2}{y}={e}^{{{x}^{3}}}$$

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Malena

$$y'-3x^2y= e^(x^3)$$
$$\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}-{3}{x}^{2}{y}={e}^{{{x}^{3}}}$$
$$\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}+{P}{y}={Q}$$
$$P= -3x^2$$, $$\displaystyle{Q}={e}^{{{x}^{3}}}$$
$$\displaystyle{I}.{F}.={e}^{{\int{P}{\left.{d}{x}\right.}}}$$
$$\displaystyle={e}^{{\int-{3}\frac{{x}^{3}}{{3}}}}$$
$$\displaystyle={e}^{{-{x}^{3}}}$$
$$\displaystyle=\frac{1}{{e}^{{{x}^{3}}}}$$
$$\displaystyle{y}{\left({I}.{F}.\right)}=\int{Q}{\left({I}.{F}.\right)}{\left.{d}{x}\right.}+{C}$$
$$\displaystyle{y}\frac{1}{{e}^{{{x}^{3}}}}=\int{e}^{{{x}^{3}}}\frac{1}{{e}^{{{x}^{3}}}}{\left.{d}{x}\right.}+{C}$$