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If [(x + 1)2 f(x) – 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)2f(x) –g(x)]is the particular integral of the different...
Let x + 1 = ez so that z = log (x + 1) and x = ez – 1.
The given equation becomes
[D(D – 1) – 3D + 4]y = (ez –1)2, D = d/dz
or (D2 – 4D + 4)y = e2z – 2ez + 1
The auxiliary equation is m2 – 4m + 4 = 0
⇒ (m – 2)2 = 0
∴ C.F. = [(C1 + C2z)e2z = [C1 + C2log (x + 1)] (x +1)2.
or (D2 – 4D + 4)y = e2z – 2ez + 1
The auxiliary equation is m2 – 4m + 4 = 0
⇒ (m – 2)2 = 0
∴ C.F. = [(C1 + C2z)e2z = [C1 + C2log (x + 1)] (x +1)2.
∴ 
The correct answer is: 
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If[(x+ 1)2f(x) –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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