Question

$Resolvendo\ a\ diferencial\ :\\\\xy'+2y=x^{3}\\\\obtemos\ ...$

Answer 1

xy'+2y = x³

y' + 2/x . y = x² 

P(x) = 2/x

I = e^∫2/x dx = e^[2lnx] = e^lnx^2 = x²

x²y' + x². 2/x . y = x² . x² 

x²y' + 2x. y = x^4

d/dx(x² y) = x^4 

∫d/dx(x² y) = ∫x^4 dx

x²y = x^5/5 + C

y = (x^3)/5 + (x^-2).C


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Sepauto 
22/05/2017
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