Assertion (A): $\frac{dy}{dx} = x + \sqrt{xy}$ is not a homogeneous differential equation.
Reason (R): For $x, y > 0$ , $x + \sqrt{xy}$ is a homogeneous function.

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

R is true: $\lambda x + \sqrt{\lambda^{2}xy} = \lambda(x + \sqrt{xy})$ , degree 1.
A is true because the equation needs $F$ of degree 0, and 1 is not 0; R says only that $F$ is homogeneous, so it does not explain A.

Worth noting

A homogeneous right side is not enough: $\frac{dy}{dx} = F$ is homogeneous only when $F$ has degree 0.

Concept: Recognising a homogeneous equation
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsHomogeneous equations

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

Assertion (A): dydx=x+xy\frac{dy}{dx} = x + \sqrt{xy}dxdy​=x+xy​ is not a homogeneous differential equation.Reason (R): For x,y>0x, y > 0x,y>0, x+xyx + \sqrt{xy}x+xy​ is a homogeneous function.

Explanation

Assertion (A): $\frac{dy}{dx} = x + \sqrt{xy}$ is not a homogeneous differential equation.
Reason (R): For $x, y > 0$ , $x + \sqrt{xy}$ is a homogeneous function.