Question

a EDO dy/dx=3-2y tem como fator intregrante I=x²x.assinale a alternetiva corretaque contem a solucao

Answer 1

$y'=3-2y\\\\y'+2y=3\\\\\mu=e^{\int{2}\, dx}=e^{2x}\\\\\mu y=\int{3\mu}\, dx\\\\ye^{2x}=\int{3e^{2x}}\, dx\\\\ye^{2x}=\dfrac{3e^{2x}}{2}+c\\\\y=\dfrac32+ce^{-2x}$