Question

Solution of differential equation `dx/dy = 1/(e^{mx} - ay)` is ______ 

पर्याय

• (a + m) y = e^mx + c 

• `ye^{ax} = me^{mx} + c`

• `y = e^{mx} + ce^{-ax}`

• `(a + m)y = e^{mx} + ce^{-ax}(a + m)`

Answer 1

Solution of differential equation `dx/dy = 1/(e^{mx} - ay)` is `underline((a + m)y = e^{mx} + ce^{-ax}(a + m))`.

Explanation:

`dx/dy = 1/(e^{mx} - ay)`

⇒ `dy/dx + ay = e^{mx}`

I.F. = `e^{int a dx} = e^{ax}`

∴ solution of the given equation is

`y . e^{ax} = inte^{mx} . e^{ax} dx + c = (e^{(a + m)x})/(a + m) + c`

⇒ y = `e^{mx}/(a + m) + ce^{-ax}`

⇒ y(a + m) = `e^{mx} + c(a + m)e^{-ax}`