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If a and b are arbitrary constants, then the solution to the ordinary differential equation is
  • a)
    y = ax + b
  • b)
    y = ae–x
  • c)
    y = a sin 2x + b cos 2x
  • d)
    y = a cosh 2x + b sinh 2x
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If a and b are arbitrary constants, then the solution to the ordinary ...
The characteristic equation is m2 - 4 = 0
⇒ m = ± 2
Then the general solution is y = c1e2x + c2e- 2x
Since e2x = cosh 2x + sinh 2x and e- 2x = cosh 2x - sinh 2x
So, y = c1 (cosh 2x + sinh 2x) + c2 (cosh 2x - sinh 2x)
y = (c1 + c2) cosh 2x + (c1 - c2) sinh 2x
Suppose a = c1 + c2 and b = c1 - c2
Then the required solution is y = a cosh 2x + b sinh 2x
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Most Upvoted Answer
If a and b are arbitrary constants, then the solution to the ordinary ...
The characteristic equation is m2 - 4 = 0
⇒ m = ± 2
Then the general solution is y = c1e2x + c2e- 2x
Since e2x = cosh 2x + sinh 2x and e- 2x = cosh 2x - sinh 2x
So, y = c1 (cosh 2x + sinh 2x) + c2 (cosh 2x - sinh 2x)
y = (c1 + c2) cosh 2x + (c1 - c2) sinh 2x
Suppose a = c1 + c2 and b = c1 - c2
Then the required solution is y = a cosh 2x + b sinh 2x
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If a and b are arbitrary constants, then the solution to the ordinary differential equation isa)y = ax + bb)y = ae–xc)y = a sin 2x + b cos 2xd)y = a cosh 2x + b sinh 2xCorrect answer is option 'D'. Can you explain this answer?
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