<p>I am stuck, I have been trying to solve this question</p>
<p>dy/dx - 3y = 4x - 1</p>
<p>I know the answer, tried numerous methods, can anyone help?</p>
<p>Given a first order linear ordinary differential equation of the form dy/dx + p(x)y = q(x), first multiply both sides by the integrating factor exp(integral(p(x) dx)) = exp(-3x). This gives:</p>
<p>exp(-3x) dy/dx - 3exp(-3x) y = (4x-1) exp(-3x)
d/dx [exp(-3x) y] = (4x-1) exp(-3x)
y = exp(3x) * integral[ (4x-1) exp(-3x) dx + C]</p>
<p>yeah, actually go to artofproblemsolving.com to ask math questions. not to say CC doesnt have good mathematicians, but AoPS is the great grandaddy of math sites.</p>