(1 point) For the linear differential equation y' + 3xy = x^{3}e^{frac{-3x^{2}}{2}} the integrating factor is: r(x) = After multiplying both sides by the integrating factor and "unapplying" the product rule we get the new differential equation: d/dx [ ] = Integrating both sides we get the algebraic equation = Solving for y, the solution to the differential equation is y = Note: Use C as the constant. Note: You can earn partial credit on this problem.
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The integrating factor for a linear differential equation of the form \(y' + p(x)y = q(x)\) is \(e^{\int p(x) dx}\). Here, \(p(x) = 3x\), so the integrating factor is \(e^{\int 3x dx} = e^{1.5x^2}\). Show more…
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