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The integrating factor of the differential equation
- a)x2(x2 - 1)
- b)x2(x2 + 1)
- c)x(x2 - 1)
- d)x(x2 + 1)
Correct answer is option 'A'. Can you explain this answer?
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The integrating factor of the differential equationa)x2(x2- 1)b)x2(x2+...
Concept:
Equation of this type is known as Linear First Order Equation, whose solution is given by: y(I.F.) = ∫(Q × I.F.)dx + c whereI.F. = e∫Pdx
Equation of this type is known as Linear First Order Equation, whose solution is given by: y(I.F.) = ∫(Q × I.F.)dx + c whereI.F. = e∫Pdx
Calculation:
Given:
By comparing equation (1) with
Solving through partial fraction method
(x + 1)(x - 1)A + x(x-1)B + x(x + 1)C = 4x2 – 2
By comparing equation (1) with
Solving through partial fraction method
(x + 1)(x - 1)A + x(x-1)B + x(x + 1)C = 4x2 – 2
Ax2 – A + Bx2 – Bx + Cx2 + Cx = 4x2 – 2
(A + B + C)x2 + (C - B)x – A = 4x2 – 2
Comparing co-efficient of x2, x, and constants we get
A + B + C = 4 ……. (ii)
C – B = 0
⇒ B = C
A = 2
∵ A + B + C = 4
⇒ 2 + B + C = 4
⇒ B + C = 2
∴ B = C = 1
⇒ 2ln x + ln (x + 1) + ln (x - 1)
⇒ 2ln x + ln (x + 1) + ln (x - 1)
⇒ ln x2 + ln (x2 - 1)
⇒ ln x2(x2 - 1)
∵I.F. = e∫Pdx
⇒ I.F = x2 (x2 - 1)
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The integrating factor of the differential equationa)x2(x2- 1)b)x2(x2+ 1)c)x(x2- 1)d)x(x2+ 1)Correct answer is option 'A'. Can you explain this answer?
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