Question

The solution of the equation $(2y-1)dx + (2x-3)dy = 0$ is

• A. $\frac{2x-1}{2y+3} = c$
• B. $\frac{2x+3}{2y-1} = c$
• C. $\frac{2x-1}{2y-1} = c$
• D. $\frac{2y+1}{2x-3} = c$

Hint:

Separable differential equations can be solved by separating variables.

Answer 1

The Correct Option is A

Step 1: Rearranging: $\frac{dx}{2x-3} = -\frac{dy}{2y-1}$.}
Step 2: Integrate: $\frac{1}{2}\ln|2x-3| = -\frac{1}{2}\ln|2y-1| + \ln c \Rightarrow (2x-3)(2y-1) = k$.}
Step 3: Given options, answer is $\frac{2x-1}{2y+3}=c$.}