整理后,均可化为一阶线性方程.一阶线性方程: y' +yP(x) = Q(x)的通解为:y = [e^(-∫Pdx)]*{ ∫Q*[e^(∫Pdx)]dx +C} 1.dy/dx = y/(x+y),改写为: dx/dy = x/y +1,dx/dy -x/y =1.(将x看作是y的函数) :有P=-1/y,Q =1.-∫Pdy =lny+c1, (可 取c1 =0),[e^(-∫Pdy)]* =y, (对数的性质)按公式,有: x = y*{∫1*[e^(∫-1/ydy)] dy+C} =y*{∫[e^(-lny)]dy +C} =y*{∫1/y)dy +C}
= y... |
