Test the statement "The differential equ

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Differential Equations

Question:

Test the statement "The differential equation dy/dx = (x⁵ + y⁵) / (x⁵- y⁵) is homogeneous"

Options:

Yes

May or may not be

none of these

Correct Answer:

Yes

Explanation:

Let dy/dx = (x⁵ + y⁵) / (x⁵- y⁵) = f(x,y)

⇒f(tx,ty) = {(tx)⁵ + (ty)⁵)} / {(tx)⁵- (ty)⁵}

⇒f(tx,ty) = t⁰ {f(x,y)}

Hence, given differential equation is homogeneous differential equation.