An integrating factor for the differential equationa)emb)e-mc)e-mxd)emxCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Concept:

If a first-order linear differential equation can be expressed as,

where P and Q are either function of x or constant

And integrating factor (I.F.) is given by

I.F = e^∫Pdx

Then, The solution of the differential equation is given by,

y × e^∫Pdx= ∫Q × e^∫Pdxdx + c

where c is an integrating constant.

Calculation:

Given:

The given differential equation,

Here, P = m, Q = e^−mx

I.F = e^∫Pdx

= e^∫mdx

= e^mx