Question

What is the general soln of dy/dx=9(x^2)(y) and particular soln of dy/dx=3x^2(e^-y)

Answer 1

dy/dx = 9x^2 y
dy/y = 9x^2 dx
ln y = 3x^3 + c
y = c e^(3x^3)

Answer 2

dy/dx=3x^2(e^-y)
e^y dy = 3x^2 dx
e^y = x^3 + c
y = ln(x^3+c)

Can't provide a particular solution unless you can tell me something else about y or c.