The solution of the differential equatio

CUET Preparation Today

Start Free Mocks

Home Questions DJUCNQP86D

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Differential Equations

Question:

The solution of the differential equation dy/dx + 4y = e^-10x is-

Options:

y= -e^-10x /6+ Ce^4x

y= -e^-10x /10+ Ce^-4x

y= -e^-10x /6+ Ce^-4x

y= e^-10x /6+ Ce^-4x

Correct Answer:

y= -e^-10x /6+ Ce^-4x

Explanation:

The given differential equation is dy/dx + 4y = e^-10x

which is of the form dy/dx + py =Q (Where p= 4 and Q=e^-10x )

Now, I.F. = e^∫pdx

I.F. = e^∫4dx

So. I.F. = e^4x

The solution is given by:

y.(I.F.) = ∫Q x(I.F.)dx +C

⇒ y.e^4x = ∫(e^-10x x e^4x) dx +C

so. y= -e^-10x /6+ Ce^-4x