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

Category: QuestionsFind the general solution of the differential equation $$\frac{dy}{dx}=\frac{y-3}{x-3}$$ (x, y≠3).
Editor">Editor Staff asked 11 months ago

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
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options
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Editor">Editor Staff answered 11 months ago

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)+log⁡C1

log⁡(y-3)-log⁡(x-3)=log⁡C1

log⁡(\frac{y-3}{x-3})=log⁡C1

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

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