Find the general solution of the differential equation \(\frac{dy}{dx}=\frac{y-3}{x-3}\) (x, y≠3).

(a) x-3=0

(b) y-3=0

(c) y+3=0

(d) x-3y=0

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Asked question is from Methods of Solving First Order & First Degree Differential Equations in chapter Differential Equations of Mathematics – Class 12

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Right option is (b) y-3=0

To explain: Given that, \frac{dy}{dx}=\frac{y-3}{x-3}

Separating the variables, we get

\frac{dy}{y-3}=\frac{dx}{x-3}

log(y-3)=log(x-3)+logC1

log(y-3)-log(x-3)=logC1

log(\frac{y-3}{x-3})=logC1

\frac{1}{C_1} \frac{y-3}{x-3}=0

y-3=0 is the general solution for the given differential equation.