The discussion revolves around the evaluation of four mathematical statements regarding differential equations and their solutions. The correct interpretation of the statements is crucial for determining their validity. Specifically, statement 1.1 incorrectly suggests that if \( y' = 3y \), then \( y = e^{2x} \). Statement 1.3 incorrectly states that if \( y' = 2y \), then \( y = 2e^{2x} \). Statements 1.2 and 1.4 lack sufficient information to be evaluated properly.
PREREQUISITESStudents of mathematics, educators teaching differential equations, and anyone interested in understanding the principles of solving first-order linear differential equations.
1.1 Well, if [math]y = e^{2x}[/math] then what is y'? Now check to see if y' = 3y.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 .