Question

y'-y+4=0 решит диффер уравнение

Answer 1

$y'-y+4=0\y=uv;y'=u'v+v'u\u'v+v'u-uv=-4\u'v+u(v'-v)=-4\begin{cases}v'-v=0\u'v=-4end{cases}\frac{dv}{dx}-v=0|*frac{dx}{v}\frac{dv}{v}=dx\intfrac{dv}{v}=int dx\ln|v|=x\v=e^x\frac{du}{dx}e^x=-4|*frac{dx}{e^x}\du=-4e^{-x}dx\int du=-4int e^{-x}dx\u=4e^{-x}+C\y=4+Ce^{x}$