Question

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

Answer 1

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.