\(dy/dx= 15x^2 e^{-y}\)

\(e^ydy= 15x^2dx\) (1)

On integrating equation (1) we get

\(\int e^{y}dy= 15 \int x^{2}dx\)

\(\Rightarrow e^{y}=5x^{3}+C\) (2)

Take logarithmic on the both side if equation (2) we get

\(\ln(e^y)= \ln(abs(5x^3+c))\)

\(\Rightarrow y \ln(e)=\ln(abs(5x^3+c))\)

\(\Rightarrow y= \ln(abs(5x^3+c))\)

\(y(x)=\ln(abs(5x^3+c))\)