MHB Which of the following statements is true?

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The discussion focuses on evaluating the truth of several mathematical statements regarding differential equations. Participants analyze the validity of each statement by checking the derivatives and the conditions provided. It is noted that some statements lack sufficient information to determine their truth. Specifically, statements 1.1 and 1.3 are examined for correctness based on their derivatives, while 1.2 and 1.4 are criticized for missing details. The conversation encourages further attempts to solve the equations for clarity.
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) Which one of the following statements is true?
1.1) If y^'=3y. Then y=e^2x .
1.2) If Then y=ce^kx for some constants c≠1 and k≠1.
1.3) If y^'=2y. Then y=2e^2x is .
1.4) If Then y=ce^x for some constant c .
 
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Sam Fuller said:
) Which one of the following statements is true?
1.1) If y^'=3y. Then y=e^2x .
1.2) If Then y=ce^kx for some constants c≠1 and k≠1.
1.3) If y^'=2y. Then y=2e^2x is .
1.4) If Then y=ce^x for some constant c .
1.1 Well, if [math]y = e^{2x}[/math] then what is y'? Now check to see if y' = 3y.
1.2 Is missing information. There is no question asked here.
1.3 Again, given y, what is y' ?
1.4. Is missing information again.

Please make an attempt to solve these and please get back to us if you get stuck.

-Dan
 
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