Read the two statements and choose the correct option.
I. $y = Ae^{x}$ , $A$ arbitrary, is the general solution of $\frac{dy}{dx} = y$ .
II. $y = 2e^{x}$ is a particular solution of $\frac{dy}{dx} = y$ .

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

I: $\frac{d}{dx}(Ae^{x}) = Ae^{x} = y$ for every $A$ , and an order-1 equation needs one constant. True.
II: $A = 2$ is one choice of the constant, so it is a particular solution. True.

Ten questions from Differential Equations, at your own pace.

Ten questions from Differential Equations, at your own pace.

Read the two statements and choose the correct option.I. y=Aexy = Ae^{x}y=Aex, AAA arbitrary, is the general solution of dydx=y\frac{dy}{dx} = ydxdy​=y.II. y=2exy = 2e^{x}y=2ex is a particular solution of dydx=y\frac{dy}{dx} = ydxdy​=y.