how do you integrate [tex]\frac{dy}{dx}=4x-2y[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

I don't know if this is right, but this is where I'm going with this:

[tex]y'=4x-2y[/tex]

[tex]y'+2y=4x[/tex]

Solving homogeneous for complementary solution:

[tex]y'+2y=0[/tex]

Solving auxiliary equation:

[tex]m+2=0[/tex]

[tex]m=-2[/tex]

Which gives

[tex]y=c_{1}e^{-2x}[/tex]

[tex]y'=-2c_{1}e^{-2x}[/tex]

Now solving original D.E.: [tex]y'+2y=4x[/tex]

[tex]-2c_{1}e^{-2x}+2(c_{1}e^{-2x})=4x[/tex]

I'm lost at this step.

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# Need help integrating

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