If[(x+ 1)2f(x) andndash;g(x)]is the particular integral of the differential equation,a)b)c)d)Correct answer is option 'D'. Can you explain this answer?

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If [(x + 1)² f(x) – g(x)] is the particular integral of the differential equation,

Correct answer is option 'D'. Can you explain this answer?

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Differential Equation MCQ Level - 2

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If[(x+ 1)2f(x) –g(x)]is the particular integral of the different...

Let x + 1 = e^z so that z = log (x + 1) and x = e^z – 1.

The given equation becomes

[D(D – 1) – 3D + 4]y = (e^z –1)², D = d/dz
or (D² – 4D + 4)y = e^_2z – 2e^z + 1
The auxiliary equation is m² – 4m + 4 = 0
⇒ (m – 2)² = 0
∴ C.F. = [(C₁ + C₂z)e^2z = [C₁ + C₂log (x + 1)] (x +1)².

∴

The correct answer is:

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