Read the two statements and choose the correct option. I. After y = vx, a homogeneous equation becomes xdv/dx = F(v) - v. II. The solution of a homogeneous equation is always a straight line through the origin.

Homogeneous & Linear Differential Equations · Question 37 of 120

Question 37

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Read the two statements and choose the correct option.
I. After $y = vx$ , a homogeneous equation becomes $x\frac{dv}{dx} = F(v) - v$ .
II. The solution of a homogeneous equation is always a straight line through the origin.

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

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CorrectNot quiteAnswer A

Correct answer: A

I: $v + x\frac{dv}{dx} = F(v)$ , rearranged. True.
II: $y = x\log\lvert x \rvert + Cx$ , the solution of $\frac{dy}{dx} = \frac{x + y}{x}$ , is no line. False.

Ten questions from Homogeneous & Linear Differential Equations, at your own pace.

Ten questions from Homogeneous & Linear Differential Equations, at your own pace.