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The differential equationis valid in the domain 0 ≤ x ≤ 1 with y (0) = 2.25 The solution of the differential equation is
  • a)
    y = e-4x + 5
  • b)
    y = e-4x + 1.25
  • c)
    y= e4x + 5
  • d)
    y= e4x + 1.25
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The differential equationis valid in the domain 0 ≤ x ≤ 1 with y...
Concept:
If the differential equation is in the form of:

Integrating factor: 
IF = e∫Pdx
Solution for equation:
y(IF) = ∫(IF)Qdx + C
Calculation:
where 0 ≤ x ≤ 1 and y (0) = 2.25
This differential equation is in the linear form,

Where P = 4, Q = 5
∴ IF = e∫Pdx = e∫4dx = e4x
Solution of differential equation

Using y (0) = 2.25

c = 1
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The differential equationis valid in the domain 0 ≤ x ≤ 1 with y (0) = 2.25 The solution of the differential equation isa)y = e-4x+ 5b)y = e-4x+ 1.25c)y= e4x+ 5d)y= e4x+ 1.25Correct answer is option 'B'. Can you explain this answer?
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