The solution of the differential equatio

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Differential Equations

Question:

The solution of the differential equation x⁵(dy/dx) = -y⁵ will be-

Options:

x^-4+ 2y^-4 =C

x^-4+ 5y^-4 =C

2x^-4+ y^-4 =C

x^-4+ y^-4 =C

Correct Answer:

x^-4+ y^-4 =C

Explanation:

The given differential equation is

x⁵(dy/dx) = -y⁵

⇒dy/y⁵ = -(dx/x⁵)

⇒dx/x⁵ + dy/y⁵ = 0

Integrating both sides, we get:

∫(dx/x⁵ } + ∫{dy/y5} = k (where k is any constat)

⇒ (x^-4/-4) +( y^-4/-4) = k

⇒ x^-4 + y^-4 = -4k

⇒ x^-4 + y^-4 = C (where C = -4k)