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
 
The question was asked in an interview for internship.
 
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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1 Answers
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.