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## Homework Statement

1st problem - is this correctly done?

[itex]\frac{dy}{dx}[/itex] = (##x^2## - 1) ##y^2## , y(0) = 1

2nd problem - I really need help with this one.

xy' - y = ##3x^2## , y(1) = 1

## The Attempt at a Solution

1st problem:

[itex]\frac{dy}{dx}[/itex] = (##x^2## - 1) ##y^2## , y(0) = 1

[itex]\frac{1}{y^2}[/itex] dy = (##x^2## - 1) dx

##y^{-2}## dy = (##x^2## -1) dx

∫##y^{-2}## dy = (##x^2## - 1) dx

##-y^{-1}## = ([itex]\frac{x^3}{3}[/itex] - x) +c

##-1^{-1}## = c

c = -1

##-y^{-1}## = ([itex]\frac{x^3}{3}[/itex] - x) - 1.

2nd problem:

xy' - y = ##3x^2## , y(1) = 1

-y + xy' = ##3x^2##

My = -1, Nx = 1

μ(x)(-y) + μ(x)(xy') = μ(x) ##3x^2##

Am I onto something here? Any help or guidelines is highly appreciated.