Solve : y''2 + y' - 6y = 0 - CUETMOCK

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Differential Equations

Question:

Solve : y''² + y' - 6y = 0

Options:

e^-3x

e^3x

e^-6x

e^6x

Correct Answer:

e^-3x

Explanation:

Put d/dx = D

D²y + Dy - 6y = 0

D² + D - 6 = 0

D² +3D - 2D - 6 = 0

D(D+3) -2(D+3) = 0

D=-3,2

for D=-3 ⇒ d/dx=-3

dy/dx=-3y

dy/y=-3dx

ln y=-3x

y=e^-3x

Similarly, solve for D=2.

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