Which of these is a solution of d^2y/dx^2 - 2dy/dx + y = 0?

Differential Equations · Question 30 of 67

Question 30

HardOriginal question

Which of these is a solution of $\frac{d^2y}{dx^2} - 2\frac{dy}{dx} + y = 0$ ?

y = e^{2 x}

Correct answerYour answer

y = x e^{x}

Correct answerYour answer

y = x^{2} e^{x}

Correct answerYour answer

y = e^{- x}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Try $y = x e^{x}$ : $y' = x e^{x} + e^{x}$ and $y'' = \left(x + 2\right) e^{x}$ .
Substituting makes both sides equal for every $x$ ; each of the others leaves something over.

Ten questions from Differential Equations, at your own pace.

Ten questions from Differential Equations, at your own pace.