Form the differential equation of the family of curves
$straight y equals Ae to the power of Bx$
where A and B are constants.

Solution

The given equation is

straight y space equals space straight A space straight e to the power of Bx

...(1)

therefore space space space space dy over dx space equals space straight A space straight B space straight e to the power of Bx space space space space space space space space or space space space space space dy over dx space equals space straight B space straight y

...(2)

open square brackets because space of space left parenthesis 1 right parenthesis close square brackets

therefore space space space fraction numerator straight d squared straight y over denominator dx squared end fraction space equals space straight B dy over dx

...(3)
From (2) and (3),

dy over dx space equals space fraction numerator straight y begin display style fraction numerator straight d squared straight y over denominator dx squared end fraction end style over denominator begin display style dy over dx end style end fraction

straight y fraction numerator straight d squared straight y over denominator dx squared end fraction space equals open parentheses dy over dx close parentheses squared

which is the required differential equation.

Some More Questions From Vector Algebra Chapter

For Daily Free Study Material Join wiredfaculty