Answer:Given differential equation,[tex]\frac{dy}{dx}+5y=7[/tex][tex]\frac{dy}{dx}=7-5y[/tex][tex]\implies \frac{dy}{7-5y}=dx[/tex]Taking integration both sides,[tex]\int \frac{dy}{7-5y}=\int dx[/tex]Put 7 - 5y = u ⇒ -5 dy = du ⇒ dy = -du/5,[tex]-\frac{1}{5} \int \frac{du}{u} = \log x + C[/tex][tex]-\frac{1}{5} \log u = \log x + C[/tex][tex]-\frac{1}{5}\log(7-5y) = \log x + C---(1)[/tex]Here, x = 0, y = 0[tex]\implies -\frac{1}{5} \log 7= C[/tex]Hence, from equation (1),[tex]-\frac{1}{5}\log(7-5y)=\log x -\frac{1}{5}log 7[/tex][tex]\log(7-5y)=\log (\frac{x}{7^\frac{1}{5}})[/tex][tex]7-5y=\frac{x}{7^\frac{1}{5}}[/tex][tex]7-\frac{x}{7^\frac{1}{5}}=5y[/tex][tex]\implies y=\frac{1}{5}(7-\frac{x}{7^\frac{1}{5}})[/tex]