Question

The general solution of \[ \log\left(\frac{dy}{dx}\right)=ax+by \] is

• A. \(e^{ax}+e^{by}=k\)
• B. \(be^{ax}+ae^{-by}=k\)
• C. \(be^{-ax}+ae^{-by}=k\)
• D. \(e^{-ax}-e^{-by}=k\)

Hint:

For equations of the form \[ \boxed{\log\left(\frac{dy}{dx}\right)=f(x)+g(y),} \] first write \[ \boxed{\frac{dy}{dx}=e^{f(x)}e^{g(y)}} \] and then separate the variables.

Answer 1

The Correct Option is B