Find the differential equation that will represent the family of curves given by (a, b: parameter):
y = e^ax

Solution

The given differential equation is

straight y equals straight e to the power of ax space space space space space space space space space space space space space space space space space space space space space space space space space space space or space space space space log space straight y space equals space log space straight e to the power of ax

therefore space space space space space space space log space straight y space space equals space straight a space straight x

...(1)
Differentiating w.r.t. x, we get,

1 over straight y dy over dx equals straight a

...(2)
From (1) and (2), we get,

log space straight y space equals space 1 over straight y dy over dx. straight x

straight x dy over dx space equals space straight y space log space straight y

which is required differential equation.

Some More Questions From Vector Algebra Chapter

For Daily Free Study Material Join wiredfaculty