Find the equation of a curve whose tange

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Differential Equations

Question:

Find the equation of a curve whose tangent at any point on it, different from origin, has slope y + (y/x).

Options:

ke^x/x

kx.e-^x

kx.e^x

ke-^x/x

Correct Answer:

kx.e^x

Explanation:

dy/dx = y + (y/x)

dy/y = (1+1/x)dx and then integrate to obtain :

y = kx.e^x